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Completely Bounded Maps And Dilations
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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:
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
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.
Book Synopsis Operator-Valued Measures, Dilations, and the Theory of Frames by : Deguang Han
Download or read book Operator-Valued Measures, Dilations, and the Theory of Frames written by Deguang Han and published by American Mathematical Soc.. This book was released on 2014-04-07 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors develop elements of a general dilation theory for operator-valued measures. Hilbert space operator-valued measures are closely related to bounded linear maps on abelian von Neumann algebras, and some of their results include new dilation results for bounded linear maps that are not necessarily completely bounded, and from domain algebras that are not necessarily abelian. In the non-cb case the dilation space often needs to be a Banach space. They give applications to both the discrete and the continuous frame theory. There are natural associations between the theory of frames (including continuous frames and framings), the theory of operator-valued measures on sigma-algebras of sets, and the theory of continuous linear maps between -algebras. In this connection frame theory itself is identified with the special case in which the domain algebra for the maps is an abelian von Neumann algebra and the map is normal (i.e. ultraweakly, or weakly, or w*) continuous.
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 192 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.
Book Synopsis Function Spaces by : Krzysztof Jarov
Download or read book Function Spaces written by Krzysztof Jarov and published by CRC Press. This book was released on 2020-08-26 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the conference on Function Spaces held at Southern Illinois University at Edwardsville, in April, 1990. It is designed to cover a wide range of topics, including spaces of analytic functions, isometries of function spaces, geometry of Banach spaces, and Banach algebras.
Book Synopsis Classical Function Theory, Operator Dilation Theory, and Machine Computation on Multiply-Connected Domains by : Jim Agler
Download or read book Classical Function Theory, Operator Dilation Theory, and Machine Computation on Multiply-Connected Domains written by Jim Agler and published by American Mathematical Soc.. This book was released on 2008 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work begins with the presentation of generalizations of the classical Herglotz Representation Theorem for holomorphic functions with positive real part on the unit disc to functions with positive real part defined on multiply-connected domains. The generalized Herglotz kernels that appear in these representation theorems are then exploited to evolve new conditions for spectral set and rational dilation conditions over multiply-connected domains. These conditions form the basis for the theoretical development of a computational procedure for probing a well-known unsolved problem in operator theory, the so called rational dilation conjecture. Arbitrary precision algorithms for computing the Herglotz kernels on circled domains are presented and analyzed. These algorithms permit an effective implementation of the computational procedure which results in a machine generated counterexample to the rational dilation conjecture.
Author :Stefania A. M. Marcantognini Publisher :American Mathematical Soc. ISBN 13 :0821803042 Total Pages :528 pages Book Rating :4.8/5 (218 download)
Book Synopsis Harmonic Analysis and Operator Theory by : Stefania A. M. Marcantognini
Download or read book Harmonic Analysis and Operator Theory written by Stefania A. M. Marcantognini and published by American Mathematical Soc.. This book was released on 1995 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: The collection covers a broad spectrum of topics, including: wavelet analysis, Haenkel operators, multimeasure theory, the boundary behavior of the Bergman kernel, interpolation theory, and Cotlar's Lemma on almost orthogonality in the context of L[superscript p] spaces and more...
Book Synopsis Theory of Quantum Information with Memory by : Mou-Hsiung Chang
Download or read book Theory of Quantum Information with Memory written by Mou-Hsiung Chang and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-08-22 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an up-to-date account of current research in quantum information theory, at the intersection of theoretical computer science, quantum physics, and mathematics. The book confronts many unprecedented theoretical challenges generated by infi nite dimensionality and memory effects in quantum communication. The book will also equip readers with all the required mathematical tools to understand these essential questions.
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)."
Book Synopsis A Glimpse at Hilbert Space Operators by : Sheldon Axler
Download or read book A Glimpse at Hilbert Space Operators written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 2011-04-13 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paul Richard Halmos, who lived a life of unbounded devotion to mathematics and to the mathematical community, died at the age of 90 on October 2, 2006. This volume is a memorial to Paul by operator theorists he inspired. Paul’sinitial research,beginning with his 1938Ph.D. thesis at the University of Illinois under Joseph Doob, was in probability, ergodic theory, and measure theory. A shift occurred in the 1950s when Paul’s interest in foundations led him to invent a subject he termed algebraic logic, resulting in a succession of papers on that subject appearing between 1954 and 1961, and the book Algebraic Logic, published in 1962. Paul’s ?rst two papers in pure operator theory appeared in 1950. After 1960 Paul’s research focused on Hilbert space operators, a subject he viewed as enc- passing ?nite-dimensional linear algebra. Beyond his research, Paul contributed to mathematics and to its community in manifold ways: as a renowned expositor, as an innovative teacher, as a tireless editor, and through unstinting service to the American Mathematical Society and to the Mathematical Association of America. Much of Paul’s in?uence ?owed at a personal level. Paul had a genuine, uncalculating interest in people; he developed an enormous number of friendships over the years, both with mathematicians and with nonmathematicians. Many of his mathematical friends, including the editors ofthisvolume,whileabsorbingabundantquantitiesofmathematicsatPaul’sknee, learned from his advice and his example what it means to be a mathematician.
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 $F_n^\infty$.
Book Synopsis Schur Parameters, Factorization and Dilation Problems by : Tiberiu Constantinescu
Download or read book Schur Parameters, Factorization and Dilation Problems written by Tiberiu Constantinescu and published by Birkhäuser. This book was released on 2012-12-06 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the ubiquity of the Schur parameters. A dilation theoretic view leads to a unified perspective on several topics where Schur parameters appear as basic cells. Together with the transmission line, their physical counter- part, they appear in scattering theory, in modeling, prediction and filtering of nonstationary processes, in signal processing, geophysics and system theory. Modeling problems are considered for certain classes of operators, interpolation problems, determinental formulae, as well as connections with certain classes of graphs where, again, the Schur parameters could play a role. Some general algorithms that explore the transmission line are also presented in this book. As a whole, the text is self-contained and it is addressed to people interested in the previously mentioned topics or connections between them.
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 2004-10-14 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Open Quantum Systems III by : Stéphane Attal
Download or read book Open Quantum Systems III written by Stéphane Attal and published by Springer Science & Business Media. This book was released on 2006-06-07 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. From a mathematical point of view, it involves a large body of knowledge. Significant progress in the understanding of such systems has been made during the last decade. These books present in a self-contained way the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications. In Volume I the Hamiltonian description of quantum open systems is discussed. This includes an introduction to quantum statistical mechanics and its operator algebraic formulation, modular theory, spectral analysis and their applications to quantum dynamical systems. Volume II is dedicated to the Markovian formalism of classical and quantum open systems. A complete exposition of noise theory, Markov processes and stochastic differential equations, both in the classical and the quantum context, is provided. These mathematical tools are put into perspective with physical motivations and applications. Volume III is devoted to recent developments and applications. The topics discussed include the non-equilibrium properties of open quantum systems, the Fermi Golden Rule and weak coupling limit, quantum irreversibility and decoherence, qualitative behaviour of quantum Markov semigroups and continual quantum measurements.
Book Synopsis Open Quantum Systems I by : Stéphane Attal
Download or read book Open Quantum Systems I written by Stéphane Attal and published by Springer Science & Business Media. This book was released on 2006 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. From a mathematical point of view, it involves a large body of knowledge. Significant progress in the understanding of such systems has been made during the last decade. These books present in a self-contained way the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications."--Publisher's description.
Book Synopsis Open Quantum Systems II by : Stéphane Attal
Download or read book Open Quantum Systems II written by Stéphane Attal and published by Springer. This book was released on 2006-08-29 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.