Invariant Subspaces Of The Shift Operator

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Invariant Subspaces Of The Shift Operator

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Author : Javad Mashreghi
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-04-23

Invariant Subspaces Of The Shift Operator written by Javad Mashreghi 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 2015-04-23 with Mathematics categories.

This volume contains the proceedings of the CRM Workshop on Invariant Subspaces of the Shift Operator, held August 26-30, 2013, at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada. The main theme of this volume is the invariant subspaces of the shift operator (or its adjoint) on certain function spaces, in particular, the Hardy space, Dirichlet space, and de Branges-Rovnyak spaces. These spaces, and the action of the shift operator on them, have turned out to be a precious tool in various questions in analysis such as function theory (Bieberbach conjecture, rigid functions, Schwarz-Pick inequalities), operator theory (invariant subspace problem, composition operator), and systems and control theory. Of particular interest is the Dirichlet space, which is one of the classical Hilbert spaces of holomorphic functions on the unit disk. From many points of view, the Dirichlet space is an interesting and challenging example of a function space. Though much is known about it, several important open problems remain, most notably the characterization of its zero sets and of its shift-invariant subspaces. This book is co-published with the Centre de Recherches Mathématiques.

Invariant Subspaces Of The Shift Operator

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Author : Javad Mashreghi
language : en
Publisher:
Release Date : 2015

Invariant Subspaces Of The Shift Operator written by Javad Mashreghi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Banach spaces categories.

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 The Shift Operator In The D Alpha Spaces

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Author : Shadrach Nshanji Kwalar
language : en
Publisher:
Release Date : 1985

Invariant Subspaces Of The Shift Operator In The D Alpha Spaces written by Shadrach Nshanji Kwalar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.

Invariant Subspaces For The Shift Operator On Some Hilbert Spaces Of Analytic Functions

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Author : Paul Stephen Bourdon
language : en
Publisher:
Release Date : 1985

Invariant Subspaces For The Shift Operator On Some Hilbert Spaces Of Analytic Functions written by Paul Stephen Bourdon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Analytic functions categories.

Treatise On The Shift Operator

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Author : N.K. Nikol'skii
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Treatise On The Shift Operator written by N.K. Nikol'skii 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.

This book is an elementary introduction to non-classical spectral theory. Mter the basic definitions and a reduction to the study of the functional model the discussion will be centered around the simplest variant of such a model which, formally speaking, comprises only the class of contraction operators with a one dimensional rank of non-unitarity (rank(I - T*T) = rank(I - TT*) = 1). The main emphasis is on the technical side of the subject, the book being mostly devoted to a development of the analytical machinery of spectral theory rather than to this discipline itself. The functional model of Sz. -Nagy and Foia§ re duces the study of general operators to an investigation of the . compression T=PSIK of the shift operator S, Sf = zf, onto coinvariant subspaces (i. e. subspaces in variant with respect to the adjoint shift S*). In the main body of the book (the "Lectures" in the proper meaning of the word) this operator acts on the Hardy space H2 and is itself a part of the operator of multiplication by the independent variable in the space L2 (in the case at hand L2 means L2(lf), If being the unit circle), this operator again being fundamental for classical spectral theory.

Invariant Subspaces Of Shift Operators For The Quarter Plane

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Author : Om Prakash Agrawal
language : en
Publisher:
Release Date : 1983

Invariant Subspaces Of Shift Operators For The Quarter Plane written by Om Prakash Agrawal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Operator theory categories.

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.

An Introduction To Models And Decompositions In Operator Theory

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Author : Carlos S. Kubrusly
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

An Introduction To Models And Decompositions In Operator Theory written by Carlos S. Kubrusly 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.

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.

Invariant Subspace Lattices For A Class Of Operators

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Author : Boon-Hua Ong
language : en
Publisher:
Release Date : 1978

Invariant Subspace Lattices For A Class Of Operators written by Boon-Hua Ong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with categories.