Similarity Problems And Completely Bounded Maps

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Similarity Problems and Completely Bounded Maps

Author : Gilles Pisier
Publisher : Springer
ISBN 13 : 3662215373
Total Pages : 170 pages
Book Rating : 4.6/5 (622 download)

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Book Synopsis Similarity Problems and Completely Bounded Maps by : Gilles Pisier

Download or read book Similarity Problems and Completely Bounded Maps written by Gilles Pisier and published by Springer. This book was released on 2013-11-11 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Completely Bounded Maps and Operator Algebras

Author : Vern Paulsen
Publisher : Cambridge University Press
ISBN 13 : 9780521816694
Total Pages : 316 pages
Book Rating : 4.8/5 (166 download)

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Book Synopsis Completely Bounded Maps and Operator Algebras by : Vern Paulsen

Download or read book Completely Bounded Maps and Operator Algebras written by Vern Paulsen and published by Cambridge University Press. This book was released on 2002 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents

Featured Reviews in Mathematical Reviews 1997-1999

Author : Donald G. Babbitt
Publisher : American Mathematical Soc.
ISBN 13 : 9780821896709
Total Pages : 762 pages
Book Rating : 4.8/5 (967 download)

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Book Synopsis Featured Reviews in Mathematical Reviews 1997-1999 by : Donald G. Babbitt

Download or read book Featured Reviews in Mathematical Reviews 1997-1999 written by Donald G. Babbitt and published by American Mathematical Soc.. This book was released on 2000-05-05 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.

Infinite Groups: Geometric, Combinatorial and Dynamical Aspects

Author : Laurent Bartholdi
Publisher : Springer Science & Business Media
ISBN 13 : 3764374470
Total Pages : 419 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Infinite Groups: Geometric, Combinatorial and Dynamical Aspects by : Laurent Bartholdi

Download or read book Infinite Groups: Geometric, Combinatorial and Dynamical Aspects written by Laurent Bartholdi and published by Springer Science & Business Media. This book was released on 2006-03-28 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics.

Handbook of the Geometry of Banach Spaces

Author :
Publisher : Elsevier
ISBN 13 : 9780080533506
Total Pages : 870 pages
Book Rating : 4.5/5 (335 download)

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Book Synopsis Handbook of the Geometry of Banach Spaces by :

Download or read book Handbook of the Geometry of Banach Spaces written by and published by Elsevier. This book was released on 2003-05-06 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of the Geometry of Banach Spaces

Operator Algebras and Their Modules

Author : David P. Blecher
Publisher : Oxford University Press
ISBN 13 : 0191523569
Total Pages : pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Operator Algebras and Their Modules by : David P. Blecher

Download or read book Operator Algebras and Their Modules written by David P. Blecher and published by Oxford University Press. This book was released on 2004-10-07 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, nonselfadjoint 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 noncommutative 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.

Recent Advances in Operator Theory

Author : A. Dijksma
Publisher : Birkhäuser
ISBN 13 : 3034883234
Total Pages : 592 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Recent Advances in Operator Theory by : A. Dijksma

Download or read book Recent Advances in Operator Theory written by A. Dijksma and published by Birkhäuser. This book was released on 2012-12-06 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of 25 papers dedicated to Israel Gohberg, an outstanding leader in operator theory. Also containing a review of his contributions to mathematics and a complete list of his publications. The book is of interest to a wide audience of pure and applied mathematicians.

Unitary Invariants in Multivariable Operator Theory

Author : Gelu Popescu
Publisher : American Mathematical Soc.
ISBN 13 : 0821843966
Total Pages : 105 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Unitary Invariants in Multivariable Operator Theory by : Gelu Popescu

Download or read book Unitary Invariants in Multivariable Operator Theory written by Gelu Popescu and published by American Mathematical Soc.. This book was released on 2009-06-05 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper concerns unitary invariants for $n$-tuples $T:=(T_1,\ldots, T_n)$ of (not necessarily commuting) bounded linear operators on Hilbert spaces. The author introduces a notion of joint numerical radius and works out its basic properties. Multivariable versions of Berger's dilation theorem, Berger-Kato-Stampfli mapping theorem, and Schwarz's lemma from complex analysis are obtained. The author studies the joint (spatial) numerical range of $T$ in connection with several unitary invariants for $n$-tuples of operators such as: right joint spectrum, joint numerical radius, euclidean operator radius, and joint spectral radius. He also proves an analogue of Toeplitz-Hausdorff theorem on the convexity of the spatial numerical range of an operator on a Hilbert space, for the joint numerical range of operators in the noncommutative analytic Toeplitz algebra $F_n^\infty$.

Quantum Functional Analysis

Author : Aleksandr I︠A︡kovlevich Khelemskiĭ
Publisher : American Mathematical Soc.
ISBN 13 : 082185254X
Total Pages : 264 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Quantum Functional Analysis by : Aleksandr I︠A︡kovlevich Khelemskiĭ

Download or read book Quantum Functional Analysis written by Aleksandr I︠A︡kovlevich Khelemskiĭ and published by American Mathematical Soc.. This book was released on 2010 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interpreting ""quantized coefficients"" as finite rank operators in a fixed Hilbert space allows the author to replace matrix computations with algebraic techniques of module theory and tensor products, thus achieving a more invariant approach to the subject.

Operator Methods in Wavelets, Tilings, and Frames

Author : Keri A. Kornelson
Publisher : American Mathematical Soc.
ISBN 13 : 1470410400
Total Pages : 177 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Operator Methods in Wavelets, Tilings, and Frames by : Keri A. Kornelson

Download or read book Operator Methods in Wavelets, Tilings, and Frames written by Keri A. Kornelson and published by American Mathematical Soc.. This book was released on 2014-10-20 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Harmonic Analysis of Frames, Wavelets, and Tilings, held April 13-14, 2013, in Boulder, Colorado. Frames were first introduced by Duffin and Schaeffer in 1952 in the context of nonharmonic Fourier series but have enjoyed widespread interest in recent years, particularly as a unifying concept. Indeed, mathematicians with backgrounds as diverse as classical and modern harmonic analysis, Banach space theory, operator algebras, and complex analysis have recently worked in frame theory. Frame theory appears in the context of wavelets, spectra and tilings, sampling theory, and more. The papers in this volume touch on a wide variety of topics, including: convex geometry, direct integral decompositions, Beurling density, operator-valued measures, and splines. These varied topics arise naturally in the study of frames in finite and infinite dimensions. In nearly all of the papers, techniques from operator theory serve as crucial tools to solving problems in frame theory. This volume will be of interest not only to researchers in frame theory but also to those in approximation theory, representation theory, functional analysis, and harmonic analysis.

Operator Theory, Functional Analysis and Applications

Author : M. Amélia Bastos
Publisher : Springer Nature
ISBN 13 : 3030519457
Total Pages : 654 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Operator Theory, Functional Analysis and Applications by : M. Amélia Bastos

Download or read book Operator Theory, Functional Analysis and Applications written by M. Amélia Bastos and published by Springer Nature. This book was released on 2021-03-31 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents 30 articles on the topic areas discussed at the 30th “International Workshop on Operator Theory and its Applications”, held in Lisbon in July 2019. The contributions include both expository essays and original research papers reflecting recent advances in the traditional IWOTA areas and emerging adjacent fields, as well as the applications of Operator Theory and Functional Analysis. The topics range from C*–algebras and Banach *–algebras, Sturm-Liouville theory, integrable systems, dilation theory, frame theory, Toeplitz, Hankel, and singular integral operators, to questions from lattice, group and matrix theories, complex analysis, harmonic analysis, and function spaces. Given its scope, the book is chiefly intended for researchers and graduate students in the areas of Operator Theory, Functional Analysis, their applications and adjacent fields.

Introduction to Operator Space Theory

Author : Gilles Pisier
Publisher : Cambridge University Press
ISBN 13 : 9780521811651
Total Pages : 492 pages
Book Rating : 4.8/5 (116 download)

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Book Synopsis Introduction to Operator Space Theory by : Gilles Pisier

Download or read book Introduction to Operator Space Theory written by Gilles Pisier and published by Cambridge University Press. This book was released on 2003-08-25 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the theory of operator spaces, emphasising applications to C*-algebras.

Lectures on Amenability

Author : Volker Runde
Publisher : Springer
ISBN 13 : 3540455604
Total Pages : 302 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Lectures on Amenability by : Volker Runde

Download or read book Lectures on Amenability written by Volker Runde and published by Springer. This book was released on 2004-10-14 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of amenability has its origins in the beginnings of modern measure theory: Does a finitely additive set function exist which is invariant under a certain group action? Since the 1940s, amenability has become an important concept in abstract harmonic analysis (or rather, more generally, in the theory of semitopological semigroups). In 1972, B.E. Johnson showed that the amenability of a locally compact group G can be characterized in terms of the Hochschild cohomology of its group algebra L^1(G): this initiated the theory of amenable Banach algebras. Since then, amenability has penetrated other branches of mathematics, such as von Neumann algebras, operator spaces, and even differential geometry. Lectures on Amenability introduces second year graduate students to this fascinating area of modern mathematics and leads them to a level from where they can go on to read original papers on the subject. Numerous exercises are interspersed in the text.

Operator Theory on Noncommutative Domains

Author : Gelu Popescu
Publisher : American Mathematical Soc.
ISBN 13 : 0821847104
Total Pages : 137 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Operator Theory on Noncommutative Domains by : Gelu Popescu

Download or read book Operator Theory on Noncommutative Domains written by Gelu Popescu and published by American Mathematical Soc.. This book was released on 2010 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Volume 205, number 964 (third of 5 numbers)."

Operators, Functions, and Systems - An Easy Reading

Author : Nikolai K. Nikolski
Publisher : American Mathematical Soc.
ISBN 13 : 0821852655
Total Pages : 439 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Operators, Functions, and Systems - An Easy Reading by : Nikolai K. Nikolski

Download or read book Operators, Functions, and Systems - An Easy Reading written by Nikolai K. Nikolski and published by American Mathematical Soc.. This book was released on 2010-10-06 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Together with the companion volume by the same author, Operators, Functions, and Systems: An Easy Reading. Volume 1: Hardy, Hankel, and Toeplitz, Mathematical Surveys and Monographs, Vol. 92, AMS, 2002, this unique work combines four major topics of modern analysis and its applications: A. Hardy classes of holomorphic functions, B. Spectral theory of Hankel and Toeplitz operators, C. Function models for linear operators and free interpolations, and D. Infinite-dimensional system theory and signal processing. This volume contains Parts C and D. Function models for linear operators and free interpolations: This is a universal topic and, indeed, is the most influential operator theory technique in the post-spectral-theorem era. In this book, its capacity is tested by solving generalized Carleson-type interpolation problems. Infinite-dimensional system theory and signal processing: This topic is the touchstone of the three previously developed techniques. The presence of this applied topic in a pure mathematics environment reflects important changes in the mathematical landscape of the last 20 years, in that the role of the main consumer and customer of harmonic, complex, and operator analysis has more and more passed from differential equations, scattering theory, and probability to control theory and signal processing. This and the companion volume are geared toward a wide audience of readers, from graduate students to professional mathematicians. They develop an elementary approach to the subject while retaining an expert level that can be applied in advanced analysis and selected applications.

Completely Bounded Maps and Dilations

Author : Vern I. Paulsen
Publisher :
ISBN 13 :
Total Pages : 214 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Completely Bounded Maps and Dilations by : Vern I. Paulsen

Download or read book Completely Bounded Maps and Dilations written by Vern I. Paulsen and published by . This book was released on 1986 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures and Exercises on Functional Analysis

Author : Александр Яковлевич Хелемский
Publisher : American Mathematical Soc.
ISBN 13 : 9780821889695
Total Pages : 496 pages
Book Rating : 4.8/5 (896 download)

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Book Synopsis Lectures and Exercises on Functional Analysis by : Александр Яковлевич Хелемский

Download or read book Lectures and Exercises on Functional Analysis written by Александр Яковлевич Хелемский and published by American Mathematical Soc.. This book was released on with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is based on courses taught by the author at Moscow State University. Compared to many other books on the subject, it is unique in that the exposition is based on extensive use of the language and elementary constructions of category theory. Among topics featured in the book are the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus. The book contains many examples illustrating the general theory presented, as well as multiple exercises that help the reader to learn the subject. It can be used as a textbook on selected topics of functional analysis and operator theory. Prerequisites include linear algebra, elements of real analysis, and elements of the theory of metric spaces.