WorldCat Identities

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
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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
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 self-contained presentation of a number of results, which relate the volume of convex bodies in n-dimensional Euclidean space and the geometry of the corresponding finite-dimensional 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 self-contained proofs of the quotient of the subspace theorem, the inverse Santalo inequality and the inverse Brunn-Minkowski 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

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

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 non-commutative 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 self-adjoint 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

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

Non-commutative vector valued Lp-spaces and completely p-summing maps by Gilles Pisier( Book )

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 super-reflexivity and some metric spaces related to computer science, as well as an outline of the recently developed theory of non-commutative 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 self-contained 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

Séminaire d'analyse fonctionelle, 1983-1984, Paris VII-VI [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

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 first-rate 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

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

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

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
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

Random Fourier Series with Applications to Harmonic Analysis. (AM-101) 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 non-Abelian 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 Dudley-Fernique 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 non-Abelian 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. (am-101) by Gilles Pisier( )

1 edition published in 1981 in English and held by 0 WorldCat member libraries worldwide

 
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The volume of convex bodies and Banach space geometryThe Volume inequalities in the geometry of Banach spaces
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

Languages
English (212)

French (14)

Spanish (4)

Danish (1)

Italian (1)

Covers
The volume of convex bodies and Banach space geometryRandom Fourier series with applications to harmonic analysisIntroduction to operator space theoryThe operator Hilbert space OH, complex interpolation, and tensor normsComplex interpolation between Hilbert, Banach and operator spacesIntroduction to the theory of operator spacesThe Volume inequalities in the geometry of Banach spaces