Similarity Problems And Completely Bounded Maps
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Similarity Problems And Completely Bounded Maps
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Author : Gilles Pisier
language : en
Publisher: Springer
Release Date : 2013-11-11
Similarity Problems And Completely Bounded Maps written by Gilles Pisier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
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.
Handbook Of The Geometry Of Banach Spaces
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Author :
language : en
Publisher: Elsevier
Release Date : 2003-05-06
Handbook Of The Geometry Of Banach Spaces written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-06 with Mathematics categories.
Handbook of the Geometry of Banach Spaces
Semigroups Of Operators Theory And Applications
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Author : A.V. Balakrishnan
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-08-01
Semigroups Of Operators Theory And Applications written by A.V. Balakrishnan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-08-01 with Mathematics categories.
These Proceedings comprise the bulk of the papers presented at the Inter national Conference on Semigroups of Opemtors: Theory and Contro~ held 14-18 December 1998, Newport Beach, California, U.S.A. The intent of the Conference was to highlight recent advances in the the ory of Semigroups of Operators which provides the abstract framework for the time-domain solutions of time-invariant boundary-value/initial-value problems of partial differential equations. There is of course a firewall between the ab stract theory and the applications and one of the Conference aims was to bring together both in the hope that it may be of value to both communities. In these days when all scientific activity is judged by its value on "dot com" it is not surprising that mathematical analysis that holds no promise of an immediate commercial product-line, or even a software tool-box, is not high in research priority. We are particularly pleased therefore that the National Science Foundation provided generous financial support without which this Conference would have been impossible to organize. Our special thanks to Dr. Kishan Baheti, Program Manager.
Operator Algebras And Applications
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Author : A. Katavolos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Operator Algebras And Applications written by A. Katavolos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
During the last few years, the theory of operator algebras, particularly non-self-adjoint operator algebras, has evolved dramatically, experiencing both international growth and interfacing with other important areas. The present volume presents a survey of some of the latest developments in the field in a form that is detailed enough to be accessible to advanced graduate students as well as researchers in the field. Among the topics treated are: operator spaces, Hilbert modules, limit algebras, reflexive algebras and subspaces, relations to basis theory, C* algebraic quantum groups, endomorphisms of operator algebras, conditional expectations and projection maps, and applications, particularly to wavelet theory. The volume also features an historical paper offering a new approach to the Pythagoreans' discovery of irrational numbers.
Advanced Techniques With Block Matrices Of Operators
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Author : Mohammad Sal Moslehian
language : en
Publisher: Springer Nature
Release Date : 2024-08-28
Advanced Techniques With Block Matrices Of Operators written by Mohammad Sal Moslehian and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-28 with Mathematics categories.
This book introduces several powerful techniques and fundamental ideas involving block matrices of operators, as well as matrices with elements in a C*-algebra. These techniques allow for the solution of problems that may be difficult to treat. Specifically, 2×2 operator matrices yield significant mathematical inequalities in various fields of operator theory and matrix analysis. The authors employ block matrices to simplify complicated problems. Operator matrices have garnered attention for their applications in quantum information and computing theories. Each chapter concludes with a diverse set of exercises and problems for readers, along with references to relevant literature. Some problems pose open questions, while others challenge readers and provide suggestions for future research. This book is suitable for an advanced undergraduate or graduate course and can be used in the classroom. It also serves as a valuable resource for researchers and students in mathematics and physics who have a basic understanding of linear algebra, functional analysis, and operator theory.
Loeb Measures In Practice Recent Advances
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Author : Nigel J. Cutland
language : en
Publisher: Springer
Release Date : 2004-10-11
Loeb Measures In Practice Recent Advances written by Nigel J. Cutland and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-11 with Mathematics categories.
This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA. Subsequent chapters sketch a range of recent applications of Loeb measures due to the author and his collaborators, in such diverse fields as (stochastic) fluid mechanics, stochastic calculus of variations ("Malliavin" calculus) and the mathematical finance theory. The exposition is designed for a general audience, and no previous knowledge of either NSA or the various fields of applications is assumed.
Tensor Products Of C Algebras And Operator Spaces
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Author : Gilles Pisier
language : en
Publisher: Cambridge University Press
Release Date : 2020-02-27
Tensor Products Of C Algebras And Operator Spaces written by Gilles Pisier and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-27 with Mathematics categories.
Presents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students.
Stability Of Operators And Operator Semigroups
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Author : Tanja Eisner
language : en
Publisher: Birkhäuser
Release Date : 2019-10-01
Stability Of Operators And Operator Semigroups written by Tanja Eisner and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-01 with Mathematics categories.
The asymptotic behaviour, in particular "stability" in some sense, is studied systematically for discrete and for continuous linear dynamical systems on Banach spaces. Of particular concern is convergence to an equilibrium with respect to various topologies. Parallels and differences between the discrete and the continuous situation are emphasised.
Operator Valued Measures Dilations And The Theory Of Frames
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Author : Deguang Han
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-04-07
Operator Valued Measures Dilations And The Theory Of Frames written by Deguang Han and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-07 with Mathematics categories.
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.
Theory Of K Loops
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Author : Hubert Kiechle
language : en
Publisher: Springer
Release Date : 2004-10-12
Theory Of K Loops written by Hubert Kiechle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-12 with Mathematics categories.
The book contains the first systematic exposition of the current known theory of K-loops, as well as some new material. In particular, big classes of examples are constructed. The theory for sharply 2-transitive groups is generalized to the theory of Frobenius groups with many involutions. A detailed discussion of the relativistic velocity addition based on the author's construction of K-loops from classical groups is also included. The first chapters of the book can be used as a text, the later chapters are research notes, and only partially suitable for the classroom. The style is concise, but complete proofs are given. The prerequisites are a basic knowledge of algebra such as groups, fields, and vector spaces with forms.