Introduction To Operator Space Theory
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Introduction To Operator Space Theory
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Author : Gilles Pisier
language : en
Publisher: Cambridge University Press
Release Date : 2003-08-25
Introduction To Operator Space Theory 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 2003-08-25 with Mathematics categories.
An introduction to the theory of operator spaces, emphasising applications to C*-algebras.
Introduction To Operator Theory In Riesz Spaces
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Author : Adriaan C. Zaanen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Operator Theory In Riesz Spaces written by Adriaan C. Zaanen 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.
Since the beginning of the thirties a considerable number of books on func tional analysis has been published. Among the first ones were those by M. H. Stone on Hilbert spaces and by S. Banach on linear operators, both from 1932. The amount of material in the field of functional analysis (in cluding operator theory) has grown to such an extent that it has become impossible now to include all of it in one book. This holds even more for text books. Therefore, authors of textbooks usually restrict themselves to normed spaces (or even to Hilbert space exclusively) and linear operators in these spaces. In more advanced texts Banach algebras and (or) topological vector spaces are sometimes included. It is only rarely, however, that the notion of order (partial order) is explicitly mentioned (even in more advanced exposi tions), although order structures occur in a natural manner in many examples (spaces of real continuous functions or spaces of measurable function~). This situation is somewhat surprising since there exist important and illuminating results for partially ordered vector spaces, in . particular for the case that the space is lattice ordered. Lattice ordered vector spaces are called vector lattices or Riesz spaces. The first results go back to F. Riesz (1929 and 1936), L. Kan torovitch (1935) and H. Freudenthal (1936).
Theory Of Operator Spaces
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Author : Edward G. Effros
language : en
Publisher: American Mathematical Society
Release Date : 2022-03-25
Theory Of Operator Spaces written by Edward G. Effros and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-25 with Mathematics categories.
This book provides the main results and ideas in the theories of completely bounded maps, operator spaces, and operator algebras, along with some of their main applications. It requires only a basic background in functional analysis to read through the book. The descriptions and discussions of the topics are self-explained. It is appropriate for graduate students new to the subject and the field. The book starts with the basic representation theorems for abstract operator spaces and their mappings, followed by a discussion of tensor products and the analogue of Grothendieck's approximation property. Next, the operator space analogues of the nuclear, integral, and absolutely summing mappings are discussed. In what is perhaps the deepest part of the book, the authors present the remarkable “non-classical” phenomena that occur when one considers local reflexivity and exactness for operator spaces. This is an area of great beauty and depth, and it represents one of the triumphs of the subject. In the final part of the book, the authors consider applications to non-commutative harmonic analysis and non-self-adjoint operator algebra theory. Operator space theory provides a synthesis of Banach space theory with the non-commuting variables of operator algebra theory, and it has led to exciting new approaches in both disciplines. This book is an indispensable introduction to the theory of operator spaces.
Operator Theory For Electromagnetics
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Author : George W. Hanson
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-10-12
Operator Theory For Electromagnetics written by George W. Hanson 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 2001-10-12 with Science categories.
This text discusses electromagnetics from the view of operator theory, in a manner more commonly seen in textbooks of quantum mechanics. It includes a self-contained introduction to operator theory, presenting definitions and theorems, plus proofs of the theorems when these are simple or enlightening.
Introduction To Operator Theory In Riesz Spaces
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Author : Adriaan C. Zaanen
language : en
Publisher: Springer
Release Date : 1997
Introduction To Operator Theory In Riesz Spaces written by Adriaan C. Zaanen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Almost no prior knowledge of functional analysis is required. For most applications some familiarity with the ordinary Lebesque integral is already sufficient. In this respect the book differs from other books on the subject. In most books on functional analysis (even excellent ones) Riesz spaces. Banach lattices and positive operators are mentioned only briefly, or even not at all.
Operator Spaces
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Author : Edward G. Effros
language : en
Publisher: Oxford University Press on Demand
Release Date : 2000
Operator Spaces written by Edward G. Effros and has been published by Oxford University Press on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
' This book is essential reading for experts in the theory of operator spaces, and for those who want to learn the banach space style advances of the last decade in operator spaces.' Bulletin of the LMSThis book combines an elementary introduction to the theory of 'quantized Banach spaces' with a discussion of some of its most surprising non-classical aspects. Only elementary notions of functional analysis are used, hence the book will be accessible to a wide range of researchers in analysis, mathematical physics, and quantum computation.
Introduction To Operator Theory
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Author : Takashi Yoshino
language : en
Publisher: CRC Press
Release Date : 1993-12-05
Introduction To Operator Theory written by Takashi Yoshino and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-05 with Mathematics categories.
An introductory exposition of the study of operator theory, presenting an interesting and rapid approach to some results which are not normally treated in an introductory source. The volume includes recent results and coverage of the current state of the field.
A Primer On Hilbert Space Theory
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Author : Carlo Alabiso
language : en
Publisher: Springer Nature
Release Date : 2021-03-03
A Primer On Hilbert Space Theory written by Carlo Alabiso and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-03 with Science categories.
This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authors’s lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.
An Introduction To Operators On The Hardy Hilbert Space
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Author : Ruben A. Martinez-Avendano
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-12
An Introduction To Operators On The Hardy Hilbert Space written by Ruben A. Martinez-Avendano 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 2007-03-12 with Mathematics categories.
This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.
Introduction To Operator Theory And Invariant Subspaces
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Author : B. Beauzamy
language : en
Publisher: Elsevier
Release Date : 1988-10-01
Introduction To Operator Theory And Invariant Subspaces written by B. Beauzamy and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-10-01 with Mathematics categories.
This monograph only requires of the reader a basic knowledge of classical analysis: measure theory, analytic functions, Hilbert spaces, functional analysis. The book is self-contained, except for a few technical tools, for which precise references are given. Part I starts with finite-dimensional spaces and general spectral theory. But very soon (Chapter III), new material is presented, leading to new directions for research. Open questions are mentioned here. Part II concerns compactness and its applications, not only spectral theory for compact operators (Invariant Subspaces and Lomonossov's Theorem) but also duality between the space of nuclear operators and the space of all operators on a Hilbert space, a result which is seldom presented. Part III contains Algebra Techniques: Gelfand's Theory, and application to Normal Operators. Here again, directions for research are indicated. Part IV deals with analytic functions, and contains a few new developments. A simplified, operator-oriented, version is presented. Part V presents dilations and extensions: Nagy-Foias dilation theory, and the author's work about C1-contractions. Part VI deals with the Invariant Subspace Problem, with positive results and counter-examples. In general, much new material is presented. On the Invariant Subspace Problem, the level of research is reached, both in the positive and negative directions.