Gilles Pisier's Books

Martingales in Banach Spaces

By: Gilles Pisier

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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.

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591

Publisher

Cambridge University Press

Published Date

ISBN 10

1316679462

ISBN 13

9781316679463

Tensor Products of C*-algebras and Operator Spaces

The Connes–Kirchberg Problem

By: Gilles Pisier

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Tensor Products of C*-algebras and Operator Spaces

The Connes–Kirchberg Problem

By: Gilles Pisier

Presents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students.

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Page Count

495

Publisher

Cambridge University Press

Published Date

ISBN 10

1108479014

ISBN 13

9781108479011

Tensor Products of C*-algebras and Operator Spaces

The Connes–Kirchberg Problem

By: Gilles Pisier

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Tensor Products of C*-algebras and Operator Spaces

The Connes–Kirchberg Problem

By: Gilles Pisier

Presents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students.

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495

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Cambridge University Press

Published Date

ISBN 10

1108479014

ISBN 13

9781108479011

Martingales in Banach Spaces

By: Gilles Pisier

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Martingales in Banach Spaces

By: Gilles Pisier

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591

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Cambridge University Press

Published Date

ISBN 10

1316679462

ISBN 13

9781316679463

Introduction to Operator Space Theory

By: Gilles Pisier

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Introduction to Operator Space Theory

By: Gilles Pisier

An introduction to the theory of operator spaces, emphasising applications to C*-algebras.

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492

Publisher

Cambridge University Press

Published Date

ISBN 10

0521811651

ISBN 13

9780521811651

Foucault

By: Gilles Deleuze

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Foucault

By: Gilles Deleuze

Examines the philosophical foundations of Foucault's writings and discusses his views on knowledge, punishment, power, and subjectivation

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Page Count

214

Publisher

U of Minnesota Press

Published Date

ISBN 10

0816616752

ISBN 13

9780816616756

Marginal and Functional Quantization of Stochastic Processes

By: Harald Luschgy,Gilles Pagès

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Marginal and Functional Quantization of Stochastic Processes

By: Harald Luschgy,Gilles Pagès

Vector Quantization, a pioneering discretization method based on nearest neighbor search, emerged in the 1950s primarily in signal processing, electrical engineering, and information theory. Later in the 1960s, it evolved into an automatic classification technique for generating prototypes of extensive datasets. In modern terms, it can be recognized as a seminal contribution to unsupervised learning through the k-means clustering algorithm in data science. In contrast, Functional Quantization, a more recent area of study dating back to the early 2000s, focuses on the quantization of continuous-time stochastic processes viewed as random vectors in Banach function spaces. This book distinguishes itself by delving into the quantization of random vectors with values in a Banach space—a unique feature of its content. Its main objectives are twofold: first, to offer a comprehensive and cohesive overview of the latest developments as well as several new results in optimal quantization theory, spanning both finite and infinite dimensions, building upon the advancements detailed in Graf and Luschgy's Lecture Notes volume. Secondly, it serves to demonstrate how optimal quantization can be employed as a space discretization method within probability theory and numerical probability, particularly in fields like quantitative finance. The main applications to numerical probability are the controlled approximation of regular and conditional expectations by quantization-based cubature formulas, with applications to time-space discretization of Markov processes, typically Brownian diffusions, by quantization trees. While primarily catering to mathematicians specializing in probability theory and numerical probability, this monograph also holds relevance for data scientists, electrical engineers involved in data transmission, and professionals in economics and logistics who are intrigued by optimal allocation problems.

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Page Count

918

Publisher

Springer Nature

Published Date

ISBN 10

3031454642

ISBN 13

9783031454646

Foucault

By: Gilles Deleuze

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Foucault

By: Gilles Deleuze

Giles Deleuze (1925-1995) was Professor of Philosophy at the University of Paris VIII. He is a key figure in poststructuralism and one of the most influential philosophers of the twentieth century. In Foucault, Deleuze presents one of the most incisive and productive analyses of the work of Michel Foucault. This is a crucial examination of the philosophical foundations and principal themes of Foucault's work, providing a rigorous engagement with Foucault's views on knowledge, punishment, power, and the nature of subjectivity. Translated by Seßn Hand. >

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Page Count

152

Publisher

A&C Black

Published Date

ISBN 10

0826490786

ISBN 13

9780826490780

Diffraction by an Immersed Elastic Wedge

By: Jean-Pierre Croisille,Gilles Lebeau

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Diffraction by an Immersed Elastic Wedge

By: Jean-Pierre Croisille,Gilles Lebeau

This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level. The type of material considered for publication includes 1. Research monographs 2. Lectures on a new field or presentations of a new angle in a classical field 3. Summer schools and intensive courses on topics of current research. Texts which are out of print but still in demand may also be considered. The timeliness of a manuscript is sometimes more important than its form, which might be preliminary or tentative. Details of the editorial policy can be found on the inside front-cover of a current volume. Manuscripts should be submitted in camera-ready form according to Springer-Verlag's specification: technical instructions will be sent on request. TEX macros may be found at: http://www.springer.de/math/authors/b- tex.html Select the version of TEX you use and then click on "Monographs". A subject index should be included. We recommend contacting the publisher or the series editors at an early stage of your project. Addresses are given on the inside back-cover.

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Page Count

146

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540668101

ISBN 13

9783540668107

Similarity Problems and Completely Bounded Maps

By: Gilles Pisier

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Similarity Problems and Completely Bounded Maps

By: Gilles Pisier

These notes revolve around three similarity problems, appearing in three dif ferent 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 open 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. For instance, we are naturally lead to study various Banach spaces formed by the matrix coefficients of group representations. Furthermore, we discuss the closely connected Schur multipliers and Grothendieck's striking characterization of those which act boundedly on B(H). 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. In some sense, completely bounded maps can also be viewed as spaces of "coefficients" of C*-algebraic representations, if we allow "B(H) valued coefficients", this is the content of the fundamental factorization property of these maps, which plays a central role in this volume. Using this notion, the three problems can all be formulated as asking whether "boundedness" implies "complete boundedness" for linear maps satisfying cer tain additional algebraic identities.

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Page Count

170

Publisher

Springer

Published Date

ISBN 10

3662215373

ISBN 13

9783662215371

The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms

By: Gilles Pisier

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The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms

By: Gilles Pisier

In the recently developed duality theory of operator spaces, bounded operators are replaced by 'completely bounded' ones, isomorphism by 'complete isomorphisms' and Banach spaces by 'operator spaces'. This allows for distinguishing between the various ways in which a given Banach space can be embedded isometrically into [italic capital]B([italic capital]H) (with H being Hilbert). One of the main results is the observation that there is a central object in this class: there is a unique self dual Hilbertian operator space (which we denote by [italic capitals]OH) which seems to play the same central role in the category of operator spaces that Hilbert spaces play in the category of Banach spaces.

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Page Count

119

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082180474X

ISBN 13

9780821804742

The Volume of Convex Bodies and Banach Space Geometry

By: Gilles Pisier

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The Volume of Convex Bodies and Banach Space Geometry

By: Gilles Pisier

A self-contained presentation of results relating the volume of convex bodies and Banach space geometry.

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Page Count

270

Publisher

Cambridge University Press

Published Date

ISBN 10

052166635X

ISBN 13

9780521666350

Book's by Gilles Pisier

Martingales in Banach Spaces

Martingales in Banach Spaces

Tensor Products of C*-algebras and Operator Spaces

Tensor Products of C*-algebras and Operator Spaces

Tensor Products of C*-algebras and Operator Spaces

Tensor Products of C*-algebras and Operator Spaces

Martingales in Banach Spaces

Martingales in Banach Spaces

Introduction to Operator Space Theory

Introduction to Operator Space Theory

Foucault

Foucault

Marginal and Functional Quantization of Stochastic Processes

Marginal and Functional Quantization of Stochastic Processes

Foucault

Foucault

Diffraction by an Immersed Elastic Wedge

Diffraction by an Immersed Elastic Wedge

Similarity Problems and Completely Bounded Maps

Similarity Problems and Completely Bounded Maps

The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms

The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms

The Volume of Convex Bodies and Banach Space Geometry

The Volume of Convex Bodies and Banach Space Geometry

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