Unitary Dilations Of Hilbert Space Operators And Related Topics
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Unitary Dilations Of Hilbert Space Operators And Related Topics
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Author : Béla Szőkefalvi-Nagy
language : en
Publisher: American Mathematical Soc.
Release Date : 1974-01-01
Unitary Dilations Of Hilbert Space Operators And Related Topics written by Béla Szőkefalvi-Nagy 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 1974-01-01 with Mathematics categories.
Unitary Dilations Of Hilbert Space Operators And Related Topics
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Author : Béla Szőkefalvi-Nagy
language : en
Publisher:
Release Date : 1974
Unitary Dilations Of Hilbert Space Operators And Related Topics written by Béla Szőkefalvi-Nagy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Characteristic functions categories.
Commutation Properties Of Hilbert Space Operators And Related Topics
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Author : Calvin R. Putnam
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Commutation Properties Of Hilbert Space Operators And Related Topics written by Calvin R. Putnam 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.
What could be regarded as the beginning of a theory of commutators AB - BA of operators A and B on a Hilbert space, considered as a dis cipline in itself, goes back at least to the two papers of Weyl [3] {1928} and von Neumann [2] {1931} on quantum mechanics and the commuta tion relations occurring there. Here A and B were unbounded self-adjoint operators satisfying the relation AB - BA = iI, in some appropriate sense, and the problem was that of establishing the essential uniqueness of the pair A and B. The study of commutators of bounded operators on a Hilbert space has a more recent origin, which can probably be pinpointed as the paper of Wintner [6] {1947}. An investigation of a few related topics in the subject is the main concern of this brief monograph. The ensuing work considers commuting or "almost" commuting quantities A and B, usually bounded or unbounded operators on a Hilbert space, but occasionally regarded as elements of some normed space. An attempt is made to stress the role of the commutator AB - BA, and to investigate its properties, as well as those of its components A and B when the latter are subject to various restrictions. Some applica tions of the results obtained are made to quantum mechanics, perturba tion theory, Laurent and Toeplitz operators, singular integral trans formations, and Jacobi matrices.
Commuting Nonselfadjoint Operators In Hilbert Space
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Author : Moshe S. Livsic
language : en
Publisher: Springer
Release Date : 2006-11-15
Commuting Nonselfadjoint Operators In Hilbert Space written by Moshe S. Livsic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Classification of commuting non-selfadjoint operators is one of the most challenging problems in operator theory even in the finite-dimensional case. The spectral analysis of dissipative operators has led to a series of deep results in the framework of unitary dilations and characteristic operator functions. It has turned out that the theory has to be based on analytic functions on algebraic manifolds and not on functions of several independent variables as was previously believed. This follows from the generalized Cayley-Hamilton Theorem, due to M.S.Livsic: "Two commuting operators with finite dimensional imaginary parts are connected in the generic case, by a certain algebraic equation whose degree does not exceed the dimension of the sum of the ranges of imaginary parts." Such investigations have been carried out in two directions. One of them, presented by L.L.Waksman, is related to semigroups of projections of multiplication operators on Riemann surfaces. Another direction, which is presented here by M.S.Livsic is based on operator colligations and collective motions of systems. Every given wave equation can be obtained as an external manifestation of collective motions. The algebraic equation mentioned above is the corresponding dispersion law of the input-output waves.
Harmonic Analysis Of Operators On Hilbert Space
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Author : B. La Sz -Nagy
language : en
Publisher:
Release Date : 2011-02-18
Harmonic Analysis Of Operators On Hilbert Space written by B. La Sz -Nagy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-18 with categories.
Topics In Operator Theory
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Author : Carl M. Pearcy
language : en
Publisher: American Mathematical Soc.
Release Date : 1974-12-31
Topics In Operator Theory written by Carl M. Pearcy 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 1974-12-31 with Mathematics categories.
Deals with various aspects of the theory of bounded linear operators on Hilbert space. This book offers information on weighted shift operators with scalar weights.
A Panorama Of Modern Operator Theory And Related Topics
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Author : Harry Dym
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-01
A Panorama Of Modern Operator Theory And Related Topics written by Harry Dym 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 2012-02-01 with Mathematics categories.
This book is dedicated to the memory of Israel Gohberg (1928–2009) – one of the great mathematicians of our time – who inspired innumerable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg’s mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory.
Recent Advances In Operator Theory And Related Topics
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Author : Laszlo Kerchy
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Recent Advances In Operator Theory And Related Topics written by Laszlo Kerchy and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
These 35 refereed articles report on recent and original results in various areas of operator theory and connected fields, many of them strongly related to contributions of Sz.-Nagy. The scientific part of the book is preceeded by fifty pages of biographical material, including several photos.
Lectures On Hyponormal Operators
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Author : Mihai Putinar
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Lectures On Hyponormal Operators written by Mihai Putinar and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The present lectures are based on a course deli vered by the authors at the Uni versi ty of Bucharest, in the winter semester 1985-1986. Without aiming at completeness, the topics selected cover all the major questions concerning hyponormal operators. Our main purpose is to provide the reader with a straightforward access to an active field of research which is strongly related to the spectral and perturbation theories of Hilbert space operators, singular integral equations and scattering theory. We have in view an audience composed especially of experts in operator theory or integral equations, mathematical physicists and graduate students. The book is intended as a reference for the basic results on hyponormal operators, but has the structure of a textbook. Parts of it can also be used as a second year graduate course. As prerequisites the reader is supposed to be acquainted with the basic principles of functional analysis and operator theory as covered for instance by Reed and Simon [1]. A t several stages of preparation of the manuscript we were pleased to benefit from proper comments made by our cOlleagues: Grigore Arsene, Tiberiu Constantinescu, Raul Curto, Jan Janas, Bebe Prunaru, Florin Radulescu, Khrysztof Rudol, Konrad Schmudgen, Florian-Horia Vasilescu. We warmly thank them all. We are indebted to Professor Israel Gohberg, the editor of this series, for his constant encouragement and his valuable mathematical advice. We wish to thank Mr. Benno Zimmermann, the Mathematics Editor at Birkhauser Verlag, for cooperation and assistance during the preparation of the manuscript.
Harmonic Analysis Of Operators On Hilbert Space
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Author : Béla Sz Nagy
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-01
Harmonic Analysis Of Operators On Hilbert Space written by Béla Sz Nagy 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 2010-09-01 with Mathematics categories.
The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.