Christian Le Merdy's Books

Operator Algebras and Their Modules

An Operator Space Approach

By: David P. Blecher,Christian Le Merdy

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Operator Algebras and Their Modules

An Operator Space Approach

By: David P. Blecher,Christian Le Merdy

This invaluable reference is the first to present the general theory of algebras of operators on a Hilbert space, and the modules over such algebras. The new theory of operator spaces is presented early on and the text assembles the basic concepts, theory and methodologies needed to equip a beginning researcher in this area. A major trend in modern mathematics, inspired largely by physics, is toward noncommutative' or quantized' phenomena. In functional analysis, this has appeared notably under the name of operator spaces', which is a variant of Banach spaces which is particularly appropriate for solving problems concerning spaces or algebras of operators on Hilbert space arising in 'noncommutative mathematics'. The category of operator spaces includes operator algebras, selfadjoint (that is, C*-algebras) or otherwise. Also, most of the important modules over operator algebras are operator spaces. A common treatment of the subjects of C*-algebras, Non-selfadjoint operator algebras, and modules over such algebras (such as Hilbert C*-modules), together under the umbrella of operator space theory, is the main topic of the book. A general theory of operator algebras, and their modules, naturally develops out of the operator space methodology. Indeed, operator space theory is a sensitive enough medium to reflect accurately many important non-commutative phenomena. Using recent advances in the field, the book shows how the underlying operator space structure captures, very precisely, the profound relations between the algebraic and the functional analytic structures involved. The rich interplay between spectral theory, operator theory, C*-algebra and von Neumann algebra techniques, and the influx of important ideas from related disciplines, such as pure algebra, Banach space theory, Banach algebras, and abstract function theory is highlighted. Each chapter ends with a lengthy section of notes containing a wealth of additional information.

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Page Count

398

Publisher

Clarendon Press

Published Date

ISBN 10

0198526598

ISBN 13

9780198526599

Functional Analytic Methods for Evolution Equations

By: Giuseppe Da Prato,Peer Christian Kunstmann,Irena Lasiecka,Alessandra Lunardi,Roland Schnaubelt,Lutz Weis

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Functional Analytic Methods for Evolution Equations

By: Giuseppe Da Prato,Peer Christian Kunstmann,Irena Lasiecka,Alessandra Lunardi,Roland Schnaubelt,Lutz Weis

This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.

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Page Count

478

Publisher

Springer

Published Date

ISBN 10

3540446532

ISBN 13

9783540446538

H[lemniscate] Functional Calculus and Square Functions on Noncommutative L[superscript P]- Spaces

By: Marius Junge,Christian Le Merdy,Quanhua Xu

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H[lemniscate] Functional Calculus and Square Functions on Noncommutative L[superscript P]- Spaces

By: Marius Junge,Christian Le Merdy,Quanhua Xu

We investigate sectorial operators and semigroups acting on noncommutative Lp-spaces. We introduce new square functions in this context and study their connection with H[infinity] functional calculus, extending some famous work by Cowling, Doust, McIntoch and Yagi concerning commutative Lp-spaces. This requires natural variants of Rademacher sectoriality and the use of the matricial structure of noncommutative Lp-spaces. We mainly focus on noncommutative diffusion semigroups. We discuss several examples of such semigroups for which we establish bounded H[infinity] functional calculus and square function estimates. This includes semigroups generated by certain Hamiltonians or Schur multipliers, q-Ornstein-Uhlenbeck semigroups acting on the q-deformed von Neumann algebras of Bozejko-Speicher, and the noncommutative Poisson semigroup acting on the group von Neumann algebra of a free group.

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Page Count

138

Published Date

ISBN 10

2856291899

ISBN 13

9782856291894

Book's by Christian Le Merdy

Operator Algebras and Their Modules

Operator Algebras and Their Modules

Functional Analytic Methods for Evolution Equations

Functional Analytic Methods for Evolution Equations

H[lemniscate] Functional Calculus and Square Functions on Noncommutative L[superscript P]- Spaces

H[lemniscate] Functional Calculus and Square Functions on Noncommutative L[superscript P]- Spaces

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