Introduction To Operator Theory And Invariant Subspaces

Author : B. Beauzamy
Publisher : Elsevier
Page : 357 pages
File Size : 53,5 Mb
Release : 1988-10-01
Category : Mathematics
ISBN : 0080960898

Get Book

Introduction to Operator Theory and Invariant Subspaces by B. Beauzamy Pdf

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.

Author : Carlos S. Kubrusly
Publisher : Springer Science & Business Media
Page : 141 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461219989

Get Book

An Introduction to Models and Decompositions in Operator Theory by Carlos S. Kubrusly Pdf

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.

Author : Heydar Radjavi,Peter Rosenthal
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642655746

Get Book

Invariant Subspaces by Heydar Radjavi,Peter Rosenthal Pdf

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.

Author : Vasile I. Istratescu
Publisher : CRC Press
Page : 605 pages
File Size : 53,9 Mb
Release : 2020-08-14
Category : Mathematics
ISBN : 9781000146325

Get Book

Introduction to Linear Operator Theory by Vasile I. Istratescu Pdf

This book is an introduction to the subject and is devoted to standard material on linear functional analysis, and presents some ergodic theorems for classes of operators containing the quasi-compact operators. It discusses various classes of operators connected with the numerical range.

Author : Anonim
Publisher : Oxford University Press
Page : 529 pages
File Size : 54,9 Mb
Release : 2023-01-30
Category : Operator theory
ISBN : 9780192863867

Get Book

Operator Theory by Example by Anonim Pdf

Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory. Rather than discuss the subject in the abstract, this textbook covers the subject through twenty examples of a wide variety of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator. The text is supplemented by over 600 end-of-chapter exercises, designed to help the reader master the topics covered in the chapter, as well as providing an opportunity to further explore the vast operator theory literature. Each chapter also contains well-researched historical facts which place each chapter within the broader context of the development of the field as a whole.

Author : Michael A. Dritschel
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 42,5 Mb
Release : 2007-06-25
Category : Mathematics
ISBN : 9783764379803

Get Book

The Extended Field of Operator Theory by Michael A. Dritschel Pdf

This volume contains contributions originating from the International Workshop on Operator Theory and Its Applications (IWOTA) held in Newcastle upon Tyne in July 2004. The articles expertly cover a broad range of material at the cutting edge of functional analysis and its applications. The works are written by world authorities in their specialities.

Author : Yuri A. Abramovich,Charalambos D. Aliprantis
Publisher : American Mathematical Soc.
Page : 546 pages
File Size : 40,6 Mb
Release : 2002
Category : Operator theory
ISBN : 9780821821466

Get Book

An Invitation to Operator Theory by Yuri A. Abramovich,Charalambos D. Aliprantis Pdf

This book offers a comprehensive and reader-friendly exposition of the theory of linear operators on Banach spaces and Banach lattices using their topological and order structures and properties. Abramovich and Aliprantis give a unique presentation that includes many new and very recent developments in operator theory and also draws together results which are spread over the vast literature. For instance, invariant subspaces of positive operators and the Daugavet equation arepresented in monograph form for the first time. The authors keep the discussion self-contained and use exercises to achieve this goal. The book contains over 600 exercises to help students master the material developed in the text. The exercises are of varying degrees of difficulty and play an importantand useful role in the exposition. They help to free the proofs of the main results of some technical details but provide students with accurate and complete accounts of how such details ought to be worked out. The exercises also contain a considerable amount of additional material that includes many well-known results whose proofs are not readily available elsewhere. The companion volume, Problems in Operator Theory, also by Abramovich and Aliprantis, is available from the AMS as Volume 51 inthe Graduate Studies in Mathematics series, and it contains complete solutions to all exercises in An Invitation to Operator Theory. The solutions demonstrate explicitly technical details in the proofs of many results in operator theory, providing the reader with rigorous and complete accounts ofsuch details. Finally, the book offers a considerable amount of additional material and further developments. By adding extra material to many exercises, the authors have managed to keep the presentation as self-contained as possible. The best way of learning mathematics is by doing mathematics, and the book Problems in Operator Theory will help achieve this goal. Prerequisites to each book are the standard introductory graduate courses in real analysis, general topology, measure theory, andfunctional analysis. An Invitation to Operator Theory is suitable for graduate or advanced courses in operator theory, real analysis, integration theory, measure theory, function theory, and functional analysis. Problems in Operator Theory is a very useful supplementary text in the above areas. Bothbooks will be of great interest to researchers and students in mathematics, as well as in physics, economics, finance, engineering, and other related areas, and will make an indispensable reference tool.

Author : Harkrishan Lal Vasudeva
Publisher : Springer
Page : 522 pages
File Size : 45,6 Mb
Release : 2017-03-27
Category : Mathematics
ISBN : 9789811030208

Get Book

Elements of Hilbert Spaces and Operator Theory by Harkrishan Lal Vasudeva Pdf

The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compression spectrum, have been worked out. Spectral theorems for self-adjoint operators, and normal operators, follow the spectral theorem for compact normal operators. The book also discusses invariant subspaces with special attention to the Volterra operator and unbounded operators. In order to make the text as accessible as possible, motivation for the topics is introduced and a greater amount of explanation than is usually found in standard texts on the subject is provided. The abstract theory in the book is supplemented with concrete examples. It is expected that these features will help the reader get a good grasp of the topics discussed. Hints and solutions to all the problems are collected at the end of the book. Additional features are introduced in the book when it becomes imperative. This spirit is kept alive throughout the book.

Author : Bhuri Singh Yadav
Publisher : Unknown
Page : 188 pages
File Size : 53,6 Mb
Release : 1990
Category : Functional analysis
ISBN : UOM:39015029719609

Get Book

Invariant Subspaces and Allied Topics by Bhuri Singh Yadav Pdf

Author : Raul E Curto,William Helton,Huaxin Lin,Xiang Tang,Rongwei Yang,Guoliang Yu
Publisher : Springer Nature
Page : 531 pages
File Size : 53,7 Mb
Release : 2020-12-12
Category : Mathematics
ISBN : 9783030433802

Get Book

Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology by Raul E Curto,William Helton,Huaxin Lin,Xiang Tang,Rongwei Yang,Guoliang Yu Pdf

This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology. Its goal is to give graduate students and researchers a relatively comprehensive overview of the current status of research in the relevant fields. The book is also a special volume dedicated to the memory of Ronald G. Douglas who passed away on February 27, 2018 at the age of 79. Many of the contributors are Douglas’ students and past collaborators. Their articles attest and commemorate his life-long contribution and influence to these fields.

Author : Takashi Yoshino
Publisher : CRC Press
Page : 168 pages
File Size : 42,6 Mb
Release : 1993-12-05
Category : Mathematics
ISBN : 0582237432

Get Book

Introduction to Operator Theory by Takashi Yoshino Pdf

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.

Author : Carlos S. Kubrusly
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 53,8 Mb
Release : 2011-03-01
Category : Mathematics
ISBN : 9780817649982

Get Book

The Elements of Operator Theory by Carlos S. Kubrusly Pdf

This second edition of Elements of Operator Theory is a concept-driven textbook that includes a significant expansion of the problems and solutions used to illustrate the principles of operator theory. Written in a user-friendly, motivating style intended to avoid the formula-computational approach, fundamental topics are presented in a systematic fashion, i.e., set theory, algebraic structures, topological structures, Banach spaces, and Hilbert spaces, culminating with the Spectral Theorem. Included in this edition: more than 150 examples, with several interesting counterexamples that demonstrate the frontiers of important theorems, as many as 300 fully rigorous proofs, specially tailored to the presentation, 300 problems, many with hints, and an additional 20 pages of problems for the second edition. *This self-contained work is an excellent text for the classroom as well as a self-study resource for researchers.

Author : Horst R. Beyer
Publisher : Springer Nature
Page : 222 pages
File Size : 40,8 Mb
Release : 2024-06-25
Category : Electronic
ISBN : 9783031490781

Get Book

Introduction to Quantum Mechanics by Horst R. Beyer Pdf

Author : Hari Bercovici
Publisher : American Mathematical Soc.
Page : 275 pages
File Size : 41,5 Mb
Release : 1988
Category : Mathematics
ISBN : 9780821815281

Get Book

Operator Theory and Arithmetic in H [infinity] by Hari Bercovici Pdf

Jordan's classification theorem for linear transformations on a finite-dimensional vector space is a natural highlight of the deep relationship between linear algebra and the arithmetical properties of polynomial rings. Because the methods and results of finite-dimensional linear algebra seldom extend to or have analogs in infinite-dimensional operator theory, it is therefore remarkable to have a class of operators which has a classification theorem analogous to Jordan's classical result and has properties closely related to the arithmetic of the ring $H^{\infty}$ of bounded analytic functions in the unit disk. $C_0$ is such a class and is the central object of study in this book.A contraction operator belongs to $C_0$ if and only if the associated functional calculus on $H^{\infty}$ has a nontrivial kernel. $C_0$ was discovered by Bela Sz.-Nagy and Ciprian Foias in their work on canonical models for contraction operators on Hilbert space. Besides their intrinsic interest and direct applications, operators of class $C_0$ are very helpful in constructing examples and counterexamples in other branches of operator theory. In addition, $C_0$ arises in certain problems of control and realization theory.In this survey work, the author provides a unified and concise presentation of a subject that was covered in many articles. The book describes the classification theory of $C_0$ and relates this class to other subjects such as general dilation theory, stochastic realization, representations of convolution algebras, and Fredholm theory. This book should be of interest to operator theorists as well as theoretical engineers interested in the applications of operator theory. In an effort to make the book as self-contained as possible, the author gives an introduction to the theory of dilations and functional models for contraction operators. Prerequisites for this book are a course in functional analysis and an acquaintance with the theory of Hardy spaces in the unit disk. In addition, knowledge of the trace class of operators is necessary in the chapter on weak contractions.

Author : Carl M. Pearcy
Publisher : American Mathematical Soc.
Page : 254 pages
File Size : 52,9 Mb
Release : 1974-12-31
Category : Mathematics
ISBN : 9780821815137

Get Book

Topics in Operator Theory by Carl M. Pearcy Pdf

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.