Sunder, V. S.
Overview
Works:  21 works in 123 publications in 3 languages and 3,233 library holdings 

Genres:  Textbooks 
Roles:  Author, Other 
Classifications:  QA326, 512.55 
Publication Timeline
.
Most widely held works by
V. S Sunder
Bounded integral operators on L²spaces by
Paul R Halmos(
Book
)
15 editions published in 1978 in English and German and held by 522 WorldCat member libraries worldwide
The subject. The phrase "integral operator" (like some other mathematically informal phrases, such as "effective procedure" and "geometric construction") is sometimes defined and sometimes not. When it is defined, the definition is likely to vary from author to author. While the definition almost always involves an integral, most of its other features can vary quite considerably. Superimposed limiting operations may enter (such as L2 limits in the theory of Fourier transforms and principal values in the theory of singular integrals), IJ' spaces and abstract Banach spaces may intervene, a scalar may be added (as in the theory of the socalled integral operators of the second kind), or, more generally, a multiplication operator may be added (as in the theory of the socalled integral operators of the third kind). The definition used in this book is the most special of all. According to it an integral operator is the natural "continuous" generali zation of the operators induced by matrices, and the only integrals that appear are the familiar LebesgueStieltjes integrals on classical nonpathological mea sure spaces. The category. Some of the flavor of the theory can be perceived in finite dimensional linear algebra. Matrices are sometimes considered to be an un natural and notationally inelegant way of looking at linear transformations. From the point of view of this book that judgement misses something
15 editions published in 1978 in English and German and held by 522 WorldCat member libraries worldwide
The subject. The phrase "integral operator" (like some other mathematically informal phrases, such as "effective procedure" and "geometric construction") is sometimes defined and sometimes not. When it is defined, the definition is likely to vary from author to author. While the definition almost always involves an integral, most of its other features can vary quite considerably. Superimposed limiting operations may enter (such as L2 limits in the theory of Fourier transforms and principal values in the theory of singular integrals), IJ' spaces and abstract Banach spaces may intervene, a scalar may be added (as in the theory of the socalled integral operators of the second kind), or, more generally, a multiplication operator may be added (as in the theory of the socalled integral operators of the third kind). The definition used in this book is the most special of all. According to it an integral operator is the natural "continuous" generali zation of the operators induced by matrices, and the only integrals that appear are the familiar LebesgueStieltjes integrals on classical nonpathological mea sure spaces. The category. Some of the flavor of the theory can be perceived in finite dimensional linear algebra. Matrices are sometimes considered to be an un natural and notationally inelegant way of looking at linear transformations. From the point of view of this book that judgement misses something
An invitation to von Neumann algebras by
V. S Sunder(
Book
)
19 editions published between 1986 and 1988 in English and held by 342 WorldCat member libraries worldwide
Why This Book: The theory of von Neumann algebras has been growing in leaps and bounds in the last 20 years. It has always had strong connections with ergodic theory and mathematical physics. It is now beginning to make contact with other areas such as differential geometry and KTheory. There seems to be a strong case for putting together a book which (a) introduces a reader to some of the basic theory needed to appreciate the recent advances, without getting bogged down by too much technical detail; (b) makes minimal assumptions on the reader's background; and (c) is small enough in size to not test the stamina and patience of the reader. This book tries to meet these requirements. In any case, it is just what its title proclaims it to be  an invitation to the exciting world of von Neumann algebras. It is hoped that after perusing this book, the reader might be tempted to fill in the numerous (and technically, capacious) gaps in this exposition, and to delve further into the depths of the theory. For the expert, it suffices to mention here that after some preliminaries, the book commences with the Murray  von Neumann classification of factors, proceeds through the basic modular theory to the III). classification of Connes, and concludes with a discussion of crossedproducts, Krieger's ratio set, examples of factors, and Takesaki's duality theorem
19 editions published between 1986 and 1988 in English and held by 342 WorldCat member libraries worldwide
Why This Book: The theory of von Neumann algebras has been growing in leaps and bounds in the last 20 years. It has always had strong connections with ergodic theory and mathematical physics. It is now beginning to make contact with other areas such as differential geometry and KTheory. There seems to be a strong case for putting together a book which (a) introduces a reader to some of the basic theory needed to appreciate the recent advances, without getting bogged down by too much technical detail; (b) makes minimal assumptions on the reader's background; and (c) is small enough in size to not test the stamina and patience of the reader. This book tries to meet these requirements. In any case, it is just what its title proclaims it to be  an invitation to the exciting world of von Neumann algebras. It is hoped that after perusing this book, the reader might be tempted to fill in the numerous (and technically, capacious) gaps in this exposition, and to delve further into the depths of the theory. For the expert, it suffices to mention here that after some preliminaries, the book commences with the Murray  von Neumann classification of factors, proceeds through the basic modular theory to the III). classification of Connes, and concludes with a discussion of crossedproducts, Krieger's ratio set, examples of factors, and Takesaki's duality theorem
Introduction to subfactors by
Vaughan F. R Jones(
Book
)
18 editions published in 1997 in English and held by 327 WorldCat member libraries worldwide
Cover; Title; Copyright; Dedication; Contents; Preface; Acknowledgement; 1 Factors; 1.1 von Neumann algebras and factors; 1.2 The standard form; 1.3 Discrete crossed products; 1.4 Examples of factors; 1.4.1 Group von Neumann algebras; 1.4.2 Crossed products of commutative von Neumann algebras; 1.4.3 Infinite tensor products; 2 Subfactors and index; 2.1 The classification of modules; 2.2 dimMH; 2.3 Subfactors and index; 3 Some basic facts; 3.1 The basic construction; 3.2 Finitedimensional inclusions; 3.3 The projections en and the tower; 4 The principal and dual graphs; 4.1 More on bimodules
18 editions published in 1997 in English and held by 327 WorldCat member libraries worldwide
Cover; Title; Copyright; Dedication; Contents; Preface; Acknowledgement; 1 Factors; 1.1 von Neumann algebras and factors; 1.2 The standard form; 1.3 Discrete crossed products; 1.4 Examples of factors; 1.4.1 Group von Neumann algebras; 1.4.2 Crossed products of commutative von Neumann algebras; 1.4.3 Infinite tensor products; 2 Subfactors and index; 2.1 The classification of modules; 2.2 dimMH; 2.3 Subfactors and index; 3 Some basic facts; 3.1 The basic construction; 3.2 Finitedimensional inclusions; 3.3 The projections en and the tower; 4 The principal and dual graphs; 4.1 More on bimodules
Functional analysis : spectral theory by
V. S Sunder(
Book
)
18 editions published between 1997 and 1998 in English and Undetermined and held by 233 WorldCat member libraries worldwide
Lectures given by the author at the Institute of Mathematical Sciences, Madras, in 1996
18 editions published between 1997 and 1998 in English and Undetermined and held by 233 WorldCat member libraries worldwide
Lectures given by the author at the Institute of Mathematical Sciences, Madras, in 1996
Topological quantum field theories from subfactors by
Vijay Kodiyalam(
Book
)
13 editions published in 2001 in English and held by 188 WorldCat member libraries worldwide
Pure mathematicians have only recently begun a rigorous study of topological quantum field theories (TQFTs). Ocneanu, in particular, showed that subfactors yield TQFTs that complement the TuraevViro construction. Until now, however, it has been difficult to find an account of this work that is both detailed and accessible. Topological Quantum Field Theories from Subfactors provides a selfcontained, explicit description of Ocneanu's construction It introduces and discusses its various ingredients with the distinct advantage of employing only genuine triangulations. The authors begin with axioms for a TQFT, go through the TuraevViro prescription for constructing such a TQFT, and finally work through Ocneanu's method of starting with a finite depth hyperfinite subfactor" and obtaining the data needed to invoke the TuraevViro machine. The authors provide a very concise treatment of finite factors of type and their bimodules and include details and calculations for all constructions. They also present, perhaps for the first time in book form, notions such as quantization functors and fusion algebras. Accessible to graduate students and others just beginning to explore this intriguing topic, Topological Quantum Field Theories from Subfactors will also be of interest to researchers in both mathematics and theoretical physics
13 editions published in 2001 in English and held by 188 WorldCat member libraries worldwide
Pure mathematicians have only recently begun a rigorous study of topological quantum field theories (TQFTs). Ocneanu, in particular, showed that subfactors yield TQFTs that complement the TuraevViro construction. Until now, however, it has been difficult to find an account of this work that is both detailed and accessible. Topological Quantum Field Theories from Subfactors provides a selfcontained, explicit description of Ocneanu's construction It introduces and discusses its various ingredients with the distinct advantage of employing only genuine triangulations. The authors begin with axioms for a TQFT, go through the TuraevViro prescription for constructing such a TQFT, and finally work through Ocneanu's method of starting with a finite depth hyperfinite subfactor" and obtaining the data needed to invoke the TuraevViro machine. The authors provide a very concise treatment of finite factors of type and their bimodules and include details and calculations for all constructions. They also present, perhaps for the first time in book form, notions such as quantization functors and fusion algebras. Accessible to graduate students and others just beginning to explore this intriguing topic, Topological Quantum Field Theories from Subfactors will also be of interest to researchers in both mathematics and theoretical physics
Measure & probability by
Siva Athreya(
Book
)
4 editions published between 2008 and 2009 in English and held by 106 WorldCat member libraries worldwide
"This book has been designed primarily for students at the masters and doctoral levels. It covers the fundamentals of measure theory and probability theory. It begins with the construction of Lebesgue measure via Caratheodory's outer measure approach and goes on to discuss integration and standard convergence theorems (monotone and dominated, as well as Fatou's lemma). An entire chapter is devoted to complex measures, L P spaces, RadonNikodym theorem and the Riesz representation theorem. The elements of probability theory (random variables, distributions, independence, product measures spaces) as also the law of large numbers and central limit theorem are presented. Discrete time Markov chains, stationary distributions and limit theorems are then discussed." "Among the highlights are alternative proofs of Riesz representation theorem and the law of large numbers. Finally, the appendix treats many basic topics such as metric spaces, topological spaces and the StoneWeierstrass theorem."Jacket
4 editions published between 2008 and 2009 in English and held by 106 WorldCat member libraries worldwide
"This book has been designed primarily for students at the masters and doctoral levels. It covers the fundamentals of measure theory and probability theory. It begins with the construction of Lebesgue measure via Caratheodory's outer measure approach and goes on to discuss integration and standard convergence theorems (monotone and dominated, as well as Fatou's lemma). An entire chapter is devoted to complex measures, L P spaces, RadonNikodym theorem and the Riesz representation theorem. The elements of probability theory (random variables, distributions, independence, product measures spaces) as also the law of large numbers and central limit theorem are presented. Discrete time Markov chains, stationary distributions and limit theorems are then discussed." "Among the highlights are alternative proofs of Riesz representation theorem and the law of large numbers. Finally, the appendix treats many basic topics such as metric spaces, topological spaces and the StoneWeierstrass theorem."Jacket
Operators on Hilbert space by
V. S Sunder(
Book
)
9 editions published between 2015 and 2016 in English and held by 52 WorldCat member libraries worldwide
Annotation
9 editions published between 2015 and 2016 in English and held by 52 WorldCat member libraries worldwide
Annotation
The functional analysis of quantum information theory : a collection of notes based on lectures by Gilles Pisier, K.R. Parthasarathy,
Vern Paulsen and Andreas Winter by
Ved Prakash Gupta(
Book
)
7 editions published in 2015 in English and Undetermined and held by 34 WorldCat member libraries worldwide
This book provides readers with a concise introduction to current studies on operatoralgebras and their generalizations, operator spaces and operator systems, with a special focus on their application in quantum information science. This basic framework for the mathematical formulation of quantum information can be traced back to the mathematical work of John von Neumann, one of the pioneers of operator algebras, which forms the underpinning of most current mathematical treatments of the quantum theory, besides being one of the most dynamic areas of twentieth century functional analysis. Today, von Neumann?s foresight finds expression in the rapidly growing field of quantum information theory. These notes gather the content of lectures given by a very distinguished group of mathematicians and quantum information theorists, held at the IMSc in Chennai some years ago, and great care has been taken to present the material as a primer on the subject matter. Starting from the basic definitions of operator spaces and operator systems, this text proceeds to discuss several important theorems including Stinespring?s dilation theorem for completely positive maps and Kirchberg?s theorem on tensor products of C*algebras. It also takes a closer look at the abstract characterization of operator systems and, motivated by the requirements of different tensor products in quantum information theory, the theory of tensor products in operator systems is discussed in detail. On the quantum information side, the book offers a rigorous treatment of quantifying entanglement in bipartite quantum systems, and moves on to review four different areas in which ideas from the theory of operator systems and operator algebras play a natural role: the issue of zeroerror communication over quantum channels, the strong subadditivity property of quantum entropy, the different norms on quantum states and the corresponding induced norms on quantum channels, and, lastly, the applications of matrixvalued random variables in the quantum information setting
7 editions published in 2015 in English and Undetermined and held by 34 WorldCat member libraries worldwide
This book provides readers with a concise introduction to current studies on operatoralgebras and their generalizations, operator spaces and operator systems, with a special focus on their application in quantum information science. This basic framework for the mathematical formulation of quantum information can be traced back to the mathematical work of John von Neumann, one of the pioneers of operator algebras, which forms the underpinning of most current mathematical treatments of the quantum theory, besides being one of the most dynamic areas of twentieth century functional analysis. Today, von Neumann?s foresight finds expression in the rapidly growing field of quantum information theory. These notes gather the content of lectures given by a very distinguished group of mathematicians and quantum information theorists, held at the IMSc in Chennai some years ago, and great care has been taken to present the material as a primer on the subject matter. Starting from the basic definitions of operator spaces and operator systems, this text proceeds to discuss several important theorems including Stinespring?s dilation theorem for completely positive maps and Kirchberg?s theorem on tensor products of C*algebras. It also takes a closer look at the abstract characterization of operator systems and, motivated by the requirements of different tensor products in quantum information theory, the theory of tensor products in operator systems is discussed in detail. On the quantum information side, the book offers a rigorous treatment of quantifying entanglement in bipartite quantum systems, and moves on to review four different areas in which ideas from the theory of operator systems and operator algebras play a natural role: the issue of zeroerror communication over quantum channels, the strong subadditivity property of quantum entropy, the different norms on quantum states and the corresponding induced norms on quantum channels, and, lastly, the applications of matrixvalued random variables in the quantum information setting
Bounded integral operators on L p2 sspaces by
Paul R Halmos(
Book
)
3 editions published in 1978 in English and held by 6 WorldCat member libraries worldwide
3 editions published in 1978 in English and held by 6 WorldCat member libraries worldwide
Unitary orbits of seladjoints in some C*algebras by
V. S Sunder(
Book
)
3 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
Characterization theorems for integral operators by
V. S Sunder(
)
3 editions published in 1977 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1977 in English and held by 5 WorldCat member libraries worldwide
Bounded integral operators on L 2 spaces by
Paul R Halmos(
Book
)
2 editions published in 1978 in Undetermined and English and held by 4 WorldCat member libraries worldwide
2 editions published in 1978 in Undetermined and English and held by 4 WorldCat member libraries worldwide
Ogranichennye Integral'nye operatory v prostranstvakh L2 by
Paul R Halmos(
Book
)
1 edition published in 1985 in Russian and held by 2 WorldCat member libraries worldwide
1 edition published in 1985 in Russian and held by 2 WorldCat member libraries worldwide
Introduction to subfactors by
Vaughan F. R Jones(
)
1 edition published in 1997 in English and held by 2 WorldCat member libraries worldwide
Subfactors have been a subject of considerable research activity for about fifteen years and are known to have significant relations with other fields such as low dimensional topology and algebraic quantum field theory. These notes give an introduction to the subject suitable for a student who has only a little familiarity with the theory of Hilbert space. A new pictorial approach to subfactors is presented in a late chapter
1 edition published in 1997 in English and held by 2 WorldCat member libraries worldwide
Subfactors have been a subject of considerable research activity for about fifteen years and are known to have significant relations with other fields such as low dimensional topology and algebraic quantum field theory. These notes give an introduction to the subject suitable for a student who has only a little familiarity with the theory of Hilbert space. A new pictorial approach to subfactors is presented in a late chapter
On boundedness and $ \parallel . \parallel_ p $ by
Huzihiro Araki(
Book
)
1 edition published in 1995 in English and held by 1 WorldCat member library worldwide
1 edition published in 1995 in English and held by 1 WorldCat member library worldwide
Bounded integral operators on 12 spaces Sunder by
Paul R Halmos(
Book
)
1 edition published in 1978 in English and held by 1 WorldCat member library worldwide
1 edition published in 1978 in English and held by 1 WorldCat member library worldwide
[Lectures on operatoralgebraic Ktheory](
Book
)
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
Actions of finite hypergroups and examples by
V. S Sunder(
Book
)
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
On boundedness and [formula] continuity of second quantisation by
Huzihiro Araki(
Book
)
1 edition published in 1995 in English and held by 1 WorldCat member library worldwide
Abstract: "In this short note, we determine precisely which operators have the property that their (full, symmetric or antisymmetric) second quantisation is an operator which is bounded or belongs to one of the various Schatten ideals; we also note that in 'the interior' of the natural domain, the second quantisation is a continuous map."
1 edition published in 1995 in English and held by 1 WorldCat member library worldwide
Abstract: "In this short note, we determine precisely which operators have the property that their (full, symmetric or antisymmetric) second quantisation is an operator which is bounded or belongs to one of the various Schatten ideals; we also note that in 'the interior' of the natural domain, the second quantisation is a continuous map."
Bounded integral operators on L_1hn2 [L] spaces by
Paul R Halmos(
Book
)
1 edition published in 1978 in German and held by 1 WorldCat member library worldwide
1 edition published in 1978 in German and held by 1 WorldCat member library worldwide
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Related Identities
 Jones, Vaughan F. R. 1952 Author
 Halmos, Paul R. (Paul Richard) 19162006 Author
 Kodiyalam, Vijay Author
 Gupta, Ved Prakash Author
 Mandayam, Prabha
 Athreya, Siva 1971 Author
 Gehring, F. W.
 Thomsen, Klaus
 Araki, Huzihiro 1932 Author
 Pati, Vishwambhar
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Associated Subjects
Finite groups Functional analysis Global analysis (Mathematics) Hilbert space Hypergroups Integral operators Ktheory Lp spaces Mathematical physics Mathematics Measure theory Operator algebras Operator theory Physics Probabilities Quantum computing Quantum field theory Quantum theory Quantum theoryMathematics Spectral theory (Mathematics) Topology Von Neumann algebras