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Unitary Dilations Of Hilbert Space Operators And Related Topics
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Book Synopsis Unitary Dilations of Hilbert Space Operators and Related Topics by : Béla Szőkefalvi-Nagy
Download or read book Unitary Dilations of Hilbert Space Operators and Related Topics written by Béla Szőkefalvi-Nagy and published by American Mathematical Soc.. This book was released on 1974-01-01 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Unitary Dilations of Hilbert Space Operators and Related Topics by : Béla Szőkefalvi-Nagy
Download or read book Unitary Dilations of Hilbert Space Operators and Related Topics written by Béla Szőkefalvi-Nagy and published by American Mathematical Soc.. This book was released on 1974 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Commutation Properties of Hilbert Space Operators and Related Topics by : Calvin R. Putnam
Download or read book Commutation Properties of Hilbert Space Operators and Related Topics written by Calvin R. Putnam and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Harmonic Analysis of Operators on Hilbert Space by : Béla Sz Nagy
Download or read book Harmonic Analysis of Operators on Hilbert Space written by Béla Sz Nagy and published by Springer Science & Business Media. This book was released on 2010-09-01 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Harmonic Analysis of Operators on Hilbert Space by : B. La Sz -Nagy
Download or read book Harmonic Analysis of Operators on Hilbert Space written by B. La Sz -Nagy and published by . This book was released on 2011-02-18 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Panorama of Modern Operator Theory and Related Topics by : Harry Dym
Download or read book A Panorama of Modern Operator Theory and Related Topics written by Harry Dym and published by Springer Science & Business Media. This book was released on 2012-02-01 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Recent Advances in Operator Theory and Related Topics by : Laszlo Kerchy
Download or read book Recent Advances in Operator Theory and Related Topics written by Laszlo Kerchy and published by Birkhäuser. This book was released on 2012-12-06 with total page 719 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on Hyponormal Operators by : Mihai Putinar
Download or read book Lectures on Hyponormal Operators written by Mihai Putinar and published by Birkhäuser. This book was released on 2012-12-06 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Commutant Lifting Approach to Interpolation Problems by : Foias
Download or read book The Commutant Lifting Approach to Interpolation Problems written by Foias and published by Birkhäuser. This book was released on 2013-11-11 with total page 647 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical H interpolation theory was conceived at the beginning of the century by C. Caratheodory, L. Fejer and I. Schur. The basic method, due to Schur, in solving these problems consists in applying the Mobius transform to peel off the data. In 1967, D. Sarason encompassed these classical interpolation problems in a representation theorem of operators commuting with special contractions. Shortly after that, in 1968, B. Sz. Nagy and C. Foias obtained a purely geometrical extension of Sarason's results. Actually, their result states that operators intertwining restrictions of co-isometries can be extended, by preserving their norm, to operators intertwining these co-isometries; starring with R. G. Douglas, P. S. Muhly and C. Pearcy, this is referred to as the commutant lifting theorem. In 1957, Z. Nehari considered an L interpolation problern which in turn encompassed the same classical interpolation problems, as well as the computation of the distance of a function f in L to H . At about the sametime as Sarason's work, V. M."
Book Synopsis Topics in Operator Semigroups by : Shmuel Kantorovitz
Download or read book Topics in Operator Semigroups written by Shmuel Kantorovitz and published by Springer Science & Business Media. This book was released on 2009-10-22 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is concerned with the interplay between the theory of operator semigroups and spectral theory. The basics on operator semigroups are concisely covered in this self-contained text. Part I deals with the Hille--Yosida and Lumer--Phillips characterizations of semigroup generators, the Trotter--Kato approximation theorem, Kato’s unified treatment of the exponential formula and the Trotter product formula, the Hille--Phillips perturbation theorem, and Stone’s representation of unitary semigroups. Part II explores generalizations of spectral theory’s connection to operator semigroups.
Book Synopsis Commuting Nonselfadjoint Operators in Hilbert Space by : Moshe S. Livsic
Download or read book Commuting Nonselfadjoint Operators in Hilbert Space written by Moshe S. Livsic and published by Springer. This book was released on 2006-11-15 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Dual Algebras with Applications to Invariant Subspaces and Dilation Theory by : Hari Bercovici
Download or read book Dual Algebras with Applications to Invariant Subspaces and Dilation Theory written by Hari Bercovici and published by American Mathematical Soc.. This book was released on 1985 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of dual algebras has made tremendous progress since 1978, when Scott Brown originated some of the main ideas to solve the invariant subspace problem for subnormal operators. This book presents ideas concerning the solution of systems of simultaneous equations in the predual of a dual algebra, thereby developing a dilation theory.
Book Synopsis Dual Algebras with Applications to Invariant Subspaces and Dilation Theory by : Hari Bercovici
Download or read book Dual Algebras with Applications to Invariant Subspaces and Dilation Theory written by Hari Bercovici and published by American Mathematical Soc.. This book was released on 1985-01-01 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Selected Topics in the Geometrical Study of Differential Equations by : Niky Kamran
Download or read book Selected Topics in the Geometrical Study of Differential Equations written by Niky Kamran and published by American Mathematical Soc.. This book was released on 2002-01-01 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Models and Decompositions in Operator Theory by : Carlos S. Kubrusly
Download or read book An Introduction to Models and Decompositions in Operator Theory written by Carlos S. Kubrusly and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: By a Hilbert-space operator we mean a bounded linear transformation be tween separable complex Hilbert spaces. Decompositions and models for Hilbert-space operators have been very active research topics in operator theory over the past three decades. The main motivation behind them is the in variant subspace problem: does every Hilbert-space operator have a nontrivial invariant subspace? This is perhaps the most celebrated open question in op erator theory. Its relevance is easy to explain: normal operators have invariant subspaces (witness: the Spectral Theorem), as well as operators on finite dimensional Hilbert spaces (witness: canonical Jordan form). If one agrees that each of these (i. e. the Spectral Theorem and canonical Jordan form) is important enough an achievement to dismiss any further justification, then the search for nontrivial invariant subspaces is a natural one; and a recalcitrant one at that. Subnormal operators have nontrivial invariant subspaces (extending the normal branch), as well as compact operators (extending the finite-dimensional branch), but the question remains unanswered even for equally simple (i. e. simple to define) particular classes of Hilbert-space operators (examples: hyponormal and quasinilpotent operators). Yet the invariant subspace quest has certainly not been a failure at all, even though far from being settled. The search for nontrivial invariant subspaces has undoubtly yielded a lot of nice results in operator theory, among them, those concerning decompositions and models for Hilbert-space operators. This book contains nine chapters.
Book Synopsis Topics in the Homological Theory of Modules Over Commutative Rings by : Melvin Hochster
Download or read book Topics in the Homological Theory of Modules Over Commutative Rings written by Melvin Hochster and published by American Mathematical Soc.. This book was released on 1975-12-31 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains expository lectures by Melvin Hochster from the CBMS Regional Conference in Mathematics held at the University of Nebraska, June 1974. The lectures deal mainly with recent developments and still open questions in the homological theory of modules over commutative (usually, Noetherian) rings. A good deal of attention is given to the role ``big'' Cohen-Macaulay modules play in clearing up some of the open questions. A modest knowledge of commutative rings and familarity with (the long exact sequences for) Tor and Ext should suffice as a background for the reader.
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 458 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.
