Invariant Subspaces

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Invariant Subspaces

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Author : Heydar Radjavi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Invariant Subspaces written by Heydar Radjavi 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.

In recent years there has been a large amount of work on invariant subspaces, motivated by interest in the structure of non-self-adjoint of the results have been obtained in operators on Hilbert space. Some the context of certain general studies: the theory of the characteristic operator function, initiated by Livsic; the study of triangular models by Brodskii and co-workers; and the unitary dilation theory of Sz. Nagy and Foia!? Other theorems have proofs and interest independent of any particular structure theory. Since the leading workers in each of the structure theories have written excellent expositions of their work, (cf. Sz.-Nagy-Foia!? [1], Brodskii [1], and Gohberg-Krein [1], [2]), in this book we have concentrated on results independent of these theories. We hope that we have given a reasonably complete survey of such results and suggest that readers consult the above references for additional information. The table of contents indicates the material covered. We have restricted ourselves to operators on separable Hilbert space, in spite of the fact that most of the theorems are valid in all Hilbert spaces and many hold in Banach spaces as well. We felt that this restriction was sensible since it eases the exposition and since the separable-Hilbert space case of each of the theorems is generally the most interesting and potentially the most useful case.

Invariant Subspaces Of Matrices With Applications

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Author : Israel Gohberg
language : en
Publisher: SIAM
Release Date : 2006-03-01

Invariant Subspaces Of Matrices With Applications written by Israel Gohberg and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-01 with Mathematics categories.

This unique book addresses advanced linear algebra using invariant subspaces as the central notion and main tool. It comprehensively covers geometrical, algebraic, topological, and analytic properties of invariant subspaces, laying clear mathematical foundations for linear systems theory with a thorough treatment of analytic perturbation theory for matrix functions.

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.

Exact Solutions And Invariant Subspaces Of Nonlinear Partial Differential Equations In Mechanics And Physics

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Author : Victor A. Galaktionov
language : en
Publisher: CRC Press
Release Date : 2006-11-02

Exact Solutions And Invariant Subspaces Of Nonlinear Partial Differential Equations In Mechanics And Physics written by Victor A. Galaktionov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-02 with Mathematics categories.

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book

Invariant Subspaces And Other Topics

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Author : Apostol
language : en
Publisher: Birkhäuser
Release Date : 2013-11-21

Invariant Subspaces And Other Topics written by Apostol and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Social Science categories.

The annual Operator Theory conferences in Timigoara are conceived as a means to promote cooperation and exchange of in formation between specialists in all areas of Operator Theory. The present volume consist of papers contributed by the partici pants of the 1981 Conference. Since many of these papers contain results on the invariant subspace problem or are related to the role of invariant subspaces in the study of operators or operator systems, we thought it appropiate to mention this in the title of the volume, though the "other topics" have a wide range. As in past years, special sessions concerning other fields of Functio nal Analysis were organized at the 1981 Conference, but contri butions to these sessions are not included in the present volume. The research contracts of the Department of Mathematics of INCREST with the National Council for Sciences and Technology of Romaliia provided the means for developping the research activity in Functional Analysis; these contracts constitute the generous framework for these meetings. We want also to acknowledge the support of INCREST and the excelent organizing job done by our host - University of Timigoa ra-. Professor Dumitru Gagpar and Professor Mircea Reghig are among those people in Timigoara who contributed in an essential way to the success of the meeting.

Projections Onto Translation Invariant Subspaces Of L P G

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Author : Haskell P. Rosenthal
language : en
Publisher: American Mathematical Soc.
Release Date : 1966

Projections Onto Translation Invariant Subspaces Of L P G written by Haskell P. Rosenthal 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 1966 with Abelian groups categories.

Dual Algebras With Applications To Invariant Subspaces And Dilation Theory

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Author : Hari Bercovici
language : en
Publisher: American Mathematical Soc.
Release Date : 1985

Dual Algebras With Applications To Invariant Subspaces And Dilation Theory written by Hari Bercovici 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 1985 with Mathematics categories.

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.

Linear Algebra Done Right

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Author : Sheldon Axler
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-07-18

Linear Algebra Done Right written by Sheldon Axler 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 1997-07-18 with Mathematics categories.

This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.

Modern Approaches To The Invariant Subspace Problem

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Author : Isabelle Chalendar
language : en
Publisher: Cambridge University Press
Release Date : 2011-08-18

Modern Approaches To The Invariant Subspace Problem written by Isabelle Chalendar 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 2011-08-18 with Mathematics categories.

One of the major unsolved problems in operator theory is the fifty-year-old invariant subspace problem, which asks whether every bounded linear operator on a Hilbert space has a nontrivial closed invariant subspace. This book presents some of the major results in the area, including many that were derived within the past few years and cannot be found in other books. Beginning with a preliminary chapter containing the necessary pure mathematical background, the authors present a variety of powerful techniques, including the use of the operator-valued Poisson kernel, various forms of the functional calculus, Hardy spaces, fixed point theorems, minimal vectors, universal operators and moment sequences. The subject is presented at a level accessible to postgraduate students, as well as established researchers. It will be of particular interest to those who study linear operators and also to those who work in other areas of pure mathematics.

Dual Algebras With Applications To Invariant Subspaces And Dilation Theory

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Author : Hari Bercovici
language : en
Publisher: American Mathematical Soc.
Release Date : 1985-01-01

Dual Algebras With Applications To Invariant Subspaces And Dilation Theory written by Hari Bercovici 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 1985-01-01 with Mathematics categories.