Pisier, Gilles 1950
Overview
Works:  49 works in 273 publications in 5 languages and 4,952 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Thesis advisor, 956, Opponent, Interviewee, 958, Creator 
Classifications:  QA322.2, 515.732 
Publication Timeline
.
Most widely held works by
Gilles Pisier
Similarity problems and completely bounded maps by
Gilles Pisier(
Book
)
52 editions published between 1995 and 2004 in English and Undetermined and held by 606 WorldCat member libraries worldwide
These notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space B(H) of all bounded operators on a complex Hilbert space H. The first one deals with group representations, the second one with C* algebras and the third one with the disc algebra. We describe them in detail in the introduction which follows. This volume is devoted to the background necessary to understand these three problems, to the solutions that are known in some special cases and to numerous related concepts, results, counterexamples or extensions which their investigation has generated. While the three problems seem different, it is possible to place them in a common framework using the key concept of "complete boundedness", which we present in detail. Using this notion, the three problems can all be formulated as asking whether "boundedness" implies "complete boundedness" for linear maps satisfying certain additional algebraic identities. Two chapters have been added on the HALMOS and KADISON similarity problems
52 editions published between 1995 and 2004 in English and Undetermined and held by 606 WorldCat member libraries worldwide
These notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space B(H) of all bounded operators on a complex Hilbert space H. The first one deals with group representations, the second one with C* algebras and the third one with the disc algebra. We describe them in detail in the introduction which follows. This volume is devoted to the background necessary to understand these three problems, to the solutions that are known in some special cases and to numerous related concepts, results, counterexamples or extensions which their investigation has generated. While the three problems seem different, it is possible to place them in a common framework using the key concept of "complete boundedness", which we present in detail. Using this notion, the three problems can all be formulated as asking whether "boundedness" implies "complete boundedness" for linear maps satisfying certain additional algebraic identities. Two chapters have been added on the HALMOS and KADISON similarity problems
The volume of convex bodies and Banach space geometry by
Gilles Pisier(
Book
)
22 editions published between 1989 and 1999 in English and held by 490 WorldCat member libraries worldwide
This book aims to give a selfcontained presentation of a number of results, which relate the volume of convex bodies in ndimensional Euclidean space and the geometry of the corresponding finitedimensional normed spaces. The methods employ classical ideas from the theory of convex sets, probability theory, approximation theory and the local theory of Banach spaces. The book is in two parts. The first presents selfcontained proofs of the quotient of the subspace theorem, the inverse Santalo inequality and the inverse BrunnMinkowski inequality. The second part gives a detailed exposition of the recently introduced classes of Banach spaces of weak cotype 2 or weak type 2, and the intersection of the classes (weak Hilbert space). The book is based on courses given in Paris and in Texas
22 editions published between 1989 and 1999 in English and held by 490 WorldCat member libraries worldwide
This book aims to give a selfcontained presentation of a number of results, which relate the volume of convex bodies in ndimensional Euclidean space and the geometry of the corresponding finitedimensional normed spaces. The methods employ classical ideas from the theory of convex sets, probability theory, approximation theory and the local theory of Banach spaces. The book is in two parts. The first presents selfcontained proofs of the quotient of the subspace theorem, the inverse Santalo inequality and the inverse BrunnMinkowski inequality. The second part gives a detailed exposition of the recently introduced classes of Banach spaces of weak cotype 2 or weak type 2, and the intersection of the classes (weak Hilbert space). The book is based on courses given in Paris and in Texas
Random Fourier series with applications to harmonic analysis by
Michael B Marcus(
Book
)
17 editions published between 1981 and 1999 in English and held by 442 WorldCat member libraries worldwide
17 editions published between 1981 and 1999 in English and held by 442 WorldCat member libraries worldwide
Factorization of linear operators and geometry of Banach spaces by
Gilles Pisier(
Book
)
24 editions published between 1981 and 1987 in English and Undetermined and held by 371 WorldCat member libraries worldwide
24 editions published between 1981 and 1987 in English and Undetermined and held by 371 WorldCat member libraries worldwide
Introduction to operator space theory by
Gilles Pisier(
Book
)
19 editions published between 2003 and 2013 in English and held by 322 WorldCat member libraries worldwide
The theory of operator spaces is very recent and can be described as a noncommutative Banach space theory. An 'operator space' is simply a Banach space with an embedding into the space B(H) of all bounded operators on a Hilbert space H. The first part of this book is an introduction with emphasis on examples that illustrate various aspects of the theory. The second part is devoted to applications to C*algebras, with a systematic exposition of tensor products of C* algebras. The third (and shorter) part of the book describes applications to non selfadjoint operator algebras, and similarity problems. In particular the author's counterexample to the 'Halmos problem' is presented, as well as work on the new concept of "length" of an operator algebra. Graduate students and professional mathematicians interested in functional analysis, operator algebras and theoretical physics will find that this book has much to offer
19 editions published between 2003 and 2013 in English and held by 322 WorldCat member libraries worldwide
The theory of operator spaces is very recent and can be described as a noncommutative Banach space theory. An 'operator space' is simply a Banach space with an embedding into the space B(H) of all bounded operators on a Hilbert space H. The first part of this book is an introduction with emphasis on examples that illustrate various aspects of the theory. The second part is devoted to applications to C*algebras, with a systematic exposition of tensor products of C* algebras. The third (and shorter) part of the book describes applications to non selfadjoint operator algebras, and similarity problems. In particular the author's counterexample to the 'Halmos problem' is presented, as well as work on the new concept of "length" of an operator algebra. Graduate students and professional mathematicians interested in functional analysis, operator algebras and theoretical physics will find that this book has much to offer
The operator Hilbert space OH, complex interpolation, and tensor norms by
Gilles Pisier(
Book
)
14 editions published between 1996 and 2012 in English and held by 251 WorldCat member libraries worldwide
14 editions published between 1996 and 2012 in English and held by 251 WorldCat member libraries worldwide
Complex interpolation between Hilbert, Banach and operator spaces by
Gilles Pisier(
Book
)
15 editions published in 2010 in English and held by 192 WorldCat member libraries worldwide
15 editions published in 2010 in English and held by 192 WorldCat member libraries worldwide
Noncommutative vector valued Lpspaces and completely psumming maps by
Gilles Pisier(
Book
)
14 editions published in 1998 in 3 languages and held by 172 WorldCat member libraries worldwide
14 editions published in 1998 in 3 languages and held by 172 WorldCat member libraries worldwide
Martingales in banach spaces by
Gilles Pisier(
Book
)
8 editions published in 2016 in English and held by 93 WorldCat member libraries worldwide
This book focuses on the major applications of martingales to the geometry of Banach spaces, and a substantial discussion of harmonic analysis in Banach space valued Hardy spaces is also presented. It covers exciting links between superreflexivity and some metric spaces related to computer science, as well as an outline of the recently developed theory of noncommutative martingales, which has natural connections with quantum physics and quantum information theory. Requiring few prerequisites and providing fully detailed proofs for the main results, this selfcontained study is accessible to graduate students with a basic knowledge of real and complex analysis and functional analysis. Chapters can be read independently, with each building from the introductory notes, and the diversity of topics included also means this book can serve as the basis for a variety of graduate courses
8 editions published in 2016 in English and held by 93 WorldCat member libraries worldwide
This book focuses on the major applications of martingales to the geometry of Banach spaces, and a substantial discussion of harmonic analysis in Banach space valued Hardy spaces is also presented. It covers exciting links between superreflexivity and some metric spaces related to computer science, as well as an outline of the recently developed theory of noncommutative martingales, which has natural connections with quantum physics and quantum information theory. Requiring few prerequisites and providing fully detailed proofs for the main results, this selfcontained study is accessible to graduate students with a basic knowledge of real and complex analysis and functional analysis. Chapters can be read independently, with each building from the introductory notes, and the diversity of topics included also means this book can serve as the basis for a variety of graduate courses
Necessary and sufficient conditions for the uniform convergence of random trigonometric series by
Michael B Marcus(
Book
)
18 editions published in 1978 in 3 languages and held by 89 WorldCat member libraries worldwide
18 editions published in 1978 in 3 languages and held by 89 WorldCat member libraries worldwide
Séminaire d'analyse fonctionelle, 19831984, Paris VIIVI [sic] by Seminaire d'Analyse Fonctionnelle(
Book
)
12 editions published between 1984 and 1987 in French and English and held by 34 WorldCat member libraries worldwide
12 editions published between 1984 and 1987 in French and English and held by 34 WorldCat member libraries worldwide
Recent trends in analysis : proceedings of the conference in honor of Nikolai Nikolski, Bordeaux, 2011 by
N. K Nikolʹskiĭ(
Book
)
2 editions published in 2013 in English and held by 34 WorldCat member libraries worldwide
The volume contains the proceedings of the conference held in Bordeaux in 2011 to honor the 70th birthday of Nikolai Nikolski. It gathers some of the most relevant contributions presented, written by firstrate analysts. Below is a list of the main subjects covered: function spaces and reproducing kernels; Toeplitz and Hankel operators; spectral synthesis; spectral theory; semigroups of operators; singular integral operators; functional models; rational and meromorphic approximations; Fourier analysis; A publication of the Theta Foundation
2 editions published in 2013 in English and held by 34 WorldCat member libraries worldwide
The volume contains the proceedings of the conference held in Bordeaux in 2011 to honor the 70th birthday of Nikolai Nikolski. It gathers some of the most relevant contributions presented, written by firstrate analysts. Below is a list of the main subjects covered: function spaces and reproducing kernels; Toeplitz and Hankel operators; spectral synthesis; spectral theory; semigroups of operators; singular integral operators; functional models; rational and meromorphic approximations; Fourier analysis; A publication of the Theta Foundation
Espaces de Banach classiques et quantiques by
Bernard Maurey(
Book
)
in French and held by 11 WorldCat member libraries worldwide
in French and held by 11 WorldCat member libraries worldwide
Introduction to the theory of operator spaces by
Gilles Pisier(
Book
)
5 editions published between 2001 and 2003 in English and held by 9 WorldCat member libraries worldwide
5 editions published between 2001 and 2003 in English and held by 9 WorldCat member libraries worldwide
The Volume inequalities in the geometry of Banach spaces by
Gilles Pisier(
Book
)
1 edition published in 1989 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 1989 in English and held by 7 WorldCat member libraries worldwide
Geometría de los espacios Banach : teoría local finitodimensional : conferencias impartidas en el Departamento de Teoría
de Funciones de la Facultad de Ciencias de Zaragoza en diciembre de 1980 by
Gilles Pisier(
Book
)
4 editions published in 1983 in Spanish and held by 7 WorldCat member libraries worldwide
4 editions published in 1983 in Spanish and held by 7 WorldCat member libraries worldwide
Similarity Problems and Completely Bounded Maps : Second, Expanded Edition by
Gilles Pisier(
)
3 editions published in 2001 in English and held by 4 WorldCat member libraries worldwide
These notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space B(H) of all bounded operators on a complex Hilbert space H. The first one deals with group representations, the second one with C* algebras and the third one with the disc algebra. We describe them in detail in the introduction which follows. This volume is devoted to the background necessary to understand these three problems, to the solutions that are known in some special cases and to numerous related concepts, results, counterexamples or extensions which their investigation has generated. While the three problems seem different, it is possible to place them in a common framework using the key concept of "complete boundedness", which we present in detail. Using this notion, the three problems can all be formulated as asking whether "boundedness" implies "complete boundedness" for linear maps satisfying certain additional algebraic identities. Two chapters have been added on the HALMOS and KADISON similarity problems
3 editions published in 2001 in English and held by 4 WorldCat member libraries worldwide
These notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space B(H) of all bounded operators on a complex Hilbert space H. The first one deals with group representations, the second one with C* algebras and the third one with the disc algebra. We describe them in detail in the introduction which follows. This volume is devoted to the background necessary to understand these three problems, to the solutions that are known in some special cases and to numerous related concepts, results, counterexamples or extensions which their investigation has generated. While the three problems seem different, it is possible to place them in a common framework using the key concept of "complete boundedness", which we present in detail. Using this notion, the three problems can all be formulated as asking whether "boundedness" implies "complete boundedness" for linear maps satisfying certain additional algebraic identities. Two chapters have been added on the HALMOS and KADISON similarity problems
The operator Hilbert space OH, complex interpolation and tensor norms by
Gilles Pisier(
Book
)
2 editions published in 1996 in English and held by 1 WorldCat member library worldwide
2 editions published in 1996 in English and held by 1 WorldCat member library worldwide
Random Fourier Series with Applications to Harmonic Analysis. (AM101) by
Michael B Marcus(
)
2 editions published between 1982 and 2016 in English and held by 0 WorldCat member libraries worldwide
In this book the authors give the first necessary and sufficient conditions for the uniform convergence a.s. of random Fourier series on locally compact Abelian groups and on compact nonAbelian groups. They also obtain many related results. For example, whenever a random Fourier series converges uniformly a.s. it also satisfies the central limit theorem. The methods developed are used to study some questions in harmonic analysis that are not intrinsically random. For example, a new characterization of Sidon sets is derived.The major results depend heavily on the DudleyFernique necessary and sufficient condition for the continuity of stationary Gaussian processes and on recent work on sums of independent Banach space valued random variables. It is noteworthy that the proofs for the Abelian case immediately extend to the nonAbelian case once the proper definition of random Fourier series is made. In doing this the authors obtain new results on sums of independent random matrices with elements in a Banach space. The final chapter of the book suggests several directions for further research
2 editions published between 1982 and 2016 in English and held by 0 WorldCat member libraries worldwide
In this book the authors give the first necessary and sufficient conditions for the uniform convergence a.s. of random Fourier series on locally compact Abelian groups and on compact nonAbelian groups. They also obtain many related results. For example, whenever a random Fourier series converges uniformly a.s. it also satisfies the central limit theorem. The methods developed are used to study some questions in harmonic analysis that are not intrinsically random. For example, a new characterization of Sidon sets is derived.The major results depend heavily on the DudleyFernique necessary and sufficient condition for the continuity of stationary Gaussian processes and on recent work on sums of independent Banach space valued random variables. It is noteworthy that the proofs for the Abelian case immediately extend to the nonAbelian case once the proper definition of random Fourier series is made. In doing this the authors obtain new results on sums of independent random matrices with elements in a Banach space. The final chapter of the book suggests several directions for further research
Random fourier series with applications to harmonic analysis. (am101) by
Gilles Pisier(
)
1 edition published in 1981 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 1981 in English and held by 0 WorldCat member libraries worldwide
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Related Identities
 Marcus, Michael B. Author
 Conference Board of the Mathematical Sciences Other Editor
 Maurey, Bernard Author Editor
 Beauzamy, Bernard 1949 Editor
 Nikolʹskiĭ, N. K. (Nikolaĭ Kapitonovich)
 Borichev, Alexander A. 1963 Editor
 Davidson, Kenneth R. Editor
 Vasilescu, FlorianHoria 1941 Editor
 Kupin, Stanislas Editor
 Vasyunin, Vasily Editor
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Associated Subjects
Banach algebras Banach spaces C*algebras Convergence Distribution (Probability theory) Factorization of operators Finite fields (Algebra) Fourier series Functional analysis Harmonic analysis Hilbert space Inequalities (Mathematics) Interpolation Interpolation spaces Linear operators Local fields (Algebra) Lp spaces Mappings (Mathematics) Martingales (Mathematics) Mathematical analysis Mathematics Operator algebras Operator spaces Operator theory Random variables Representations of groups Selfadjoint operators
Alternative Names
Gilles Pisier Frans wiskundige
Gilles Pisier fransk matematikar
Gilles Pisier fransk matematiker
Gilles Pisier französischer Mathematiker
Gilles Pisier French mathematician
Gilles Pisier matemático francés
Gilles Pisier mathématicien français
Pisier, G.
Pisier, G. 1950
Пизье, Жиль
ジャイルス・ピジェ
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