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Author : Per Enflo
Publisher :
ISBN 13 :
Total Pages : 138 pages
Book Rating : 4.:/5 (493 download)
Download or read book On the Invariant Subspace Problem for Banach Spaces written by Per Enflo and published by . This book was released on 1980 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Isabelle Chalendar
Publisher : Cambridge University Press
ISBN 13 : 1139503294
Total Pages : 298 pages
Book Rating : 4.1/5 (395 download)
Download or read book Modern Approaches to the Invariant-Subspace Problem written by Isabelle Chalendar and published by Cambridge University Press. This book was released on 2011-08-18 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Vittorino Pata
Publisher : Springer Nature
ISBN 13 : 3030196704
Total Pages : 171 pages
Book Rating : 4.0/5 (31 download)
Download or read book Fixed Point Theorems and Applications written by Vittorino Pata and published by Springer Nature. This book was released on 2019-09-22 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses fixed point theory, a fascinating and far-reaching field with applications in several areas of mathematics. The content is divided into two main parts. The first, which is more theoretical, develops the main abstract theorems on the existence and uniqueness of fixed points of maps. In turn, the second part focuses on applications, covering a large variety of significant results ranging from ordinary differential equations in Banach spaces, to partial differential equations, operator theory, functional analysis, measure theory, and game theory. A final section containing 50 problems, many of which include helpful hints, rounds out the coverage. Intended for Master’s and PhD students in Mathematics or, more generally, mathematically oriented subjects, the book is designed to be largely self-contained, although some mathematical background is needed: readers should be familiar with measure theory, Banach and Hilbert spaces, locally convex topological vector spaces and, in general, with linear functional analysis.
Author : B. Beauzamy
Publisher : Elsevier
ISBN 13 : 0080960898
Total Pages : 373 pages
Book Rating : 4.0/5 (89 download)
Download or read book Introduction to Operator Theory and Invariant Subspaces written by B. Beauzamy and published by Elsevier. This book was released on 1988-10-01 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Damian Betebenner
Publisher :
ISBN 13 :
Total Pages : 70 pages
Book Rating : 4.:/5 (33 download)
Download or read book Facets of the Invariant Subspace Problem in Banach and Hilbert Spaces written by Damian Betebenner and published by . This book was released on 1993 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Peter D. Lax
Publisher : John Wiley & Sons
ISBN 13 : 1118626745
Total Pages : 451 pages
Book Rating : 4.1/5 (186 download)
Download or read book Functional Analysis written by Peter D. Lax and published by John Wiley & Sons. This book was released on 2014-08-28 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes sections on the spectral resolution and spectral representation of self adjoint operators, invariant subspaces, strongly continuous one-parameter semigroups, the index of operators, the trace formula of Lidskii, the Fredholm determinant, and more. Assumes prior knowledge of Naive set theory, linear algebra, point set topology, basic complex variable, and real variables. Includes an appendix on the Riesz representation theorem.
Author : Bhuri Singh Yadav
Publisher :
ISBN 13 :
Total Pages : 188 pages
Book Rating : 4.3/5 (91 download)
Download or read book Invariant Subspaces and Allied Topics written by Bhuri Singh Yadav and published by . This book was released on 1990 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R. Tunç Misirlioglu
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783838388298
Total Pages : 96 pages
Book Rating : 4.3/5 (882 download)
Download or read book Invariant Subspace Theorems written by R. Tunç Misirlioglu and published by LAP Lambert Academic Publishing. This book was released on 2010-08 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph concerns with the invariant subspace problem within the context of families of linear bounded operators on Banach spaces as well as families of positive operators on Banach lattices. Although it is primarily based on the PhD thesis of the author, the monograph provides further results and information on recent advances about the topic. The general invariant subspace problem concerns linear and bounded operators on infinite-dimensional complex Hilbert spaces, and asks whether there exists a closed subspace, different than the trivial ones, that is mapped to itself by such an operator. The picture that emerged after oodles of different attempts for a possible solution to this problem for a single operator has been the subject matter of an extensive amount of research over more than seven decades, and it was only in the late 1990s that the reformulation of the invariant subspace problem for families of operators, rather than a single one, attracted the mathematical community s growing attention. In this book, we are interested in giving some results concerning the invariant subspace problem for special families of operators.
Author : R. Tunç Mısırlıoğlu
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (85 download)
Download or read book Invariant Subspace Theorems for Families of Operators on Banach Spaces and Banach Lattices written by R. Tunç Mısırlıoğlu and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, the invariant subspace problem is studied for certain families of linear bounded operators on Banach spaces. We also consider families of positive operators on Banach lattices. This thesis is divided into four chapters. 0D0A In the first chapter , we give a brief history of the invariant subspace problem. Then the relation of the work in the thesis with the existing works on this subject is established. 0D0A The notion of a compact-friendly operator was introduced in 1994 by Y.A. Abramovich, C.D. Aliprantis, and 0. Burkinshaw. They proved that every non-zero locally quasinilpotent compact-friendly operator on a Dedekind complete Banach lattice has a non-trivial closed invariant ideal. In Chapter 2, we show that Dedekind completeness is not necessary and that the Banach lattice having separating orthomorphisms is sufficient. We also generalize a theorem due to R. Drnovsek in 2001 by using the concept of compact-friendliness. 0D0A In Chapter..3, we give an invariant subspace result for a semigroup of positive operators on a Banach space with a (Schauder) basis. This is a generalization of a theorem of Y.A. Abramovich, C.D. Aliprantis, and 0. Burkinshaw in 1995. This theorem states that for a positive continuous operator defined on a Banach space with a basis if it commutes with a non-zero positive locally quasinilpotent operator, then it has a non-trivial closed invariant subspace. By using the notion of weakly quasinilpotence introduced in 2004 by Z. Ercan and S. Önal, we then generalize our result to topological vector spaces with Markushevich basis. 0D0A In Chapter 4, collectively compact sets of linear bounded operators on infinite dimensional Banach spaces are studied in connection with the invariant subspace problem. We give some invariant subspace results with respect to the joint spectral radius and its local version for these sets. It is also shown, in a special case, that any collectively compact set of operators satisfies the Berger- Wang formula.
Author : Barbara MacCluer
Publisher : Springer Science & Business Media
ISBN 13 : 0387855297
Total Pages : 212 pages
Book Rating : 4.3/5 (878 download)
Download or read book Elementary Functional Analysis written by Barbara MacCluer and published by Springer Science & Business Media. This book was released on 2008-10-20 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional analysis arose in the early twentieth century and gradually, conquering one stronghold after another, became a nearly universal mathematical doctrine, not merely a new area of mathematics, but a new mathematical world view. Its appearance was the inevitable consequence of the evolution of all of nineteenth-century mathematics, in particular classical analysis and mathematical physics. Its original basis was formed by Cantor’s theory of sets and linear algebra. Its existence answered the question of how to state general principles of a broadly interpreted analysis in a way suitable for the most diverse situations. A.M. Vershik ([45], p. 438). This text evolved from the content of a one semester introductory course in fu- tional analysis that I have taught a number of times since 1996 at the University of Virginia. My students have included ?rst and second year graduate students prep- ing for thesis work in analysis, algebra, or topology, graduate students in various departments in the School of Engineering and Applied Science, and several und- graduate mathematics or physics majors. After a ?rst draft of the manuscript was completed, it was also used for an independent reading course for several und- graduates preparing for graduate school.
Author : Henry Helson
Publisher : Academic Press
ISBN 13 : 1483261522
Total Pages : 143 pages
Book Rating : 4.4/5 (832 download)
Download or read book Lectures on Invariant Subspaces written by Henry Helson and published by Academic Press. This book was released on 2013-10-22 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on Invariant Subspaces grew out of a series of lectures given gave at the University of Uppsala in the spring of 1962, and again in Berkeley the following semester. Since the subject is rather loosely defined the lecture style seemed appropriate also for this written version. The book is written for a graduate student who knows a little, but not necessarily very much, about analytic functions and about Hilbert space. The book contains 11 lectures and begins with a discussion of analytic functions. This is followed by lectures covering invariant subspaces, individual theorems, invariant subspaces in Lp, invariant subspaces in the line, and analytic vector functions. Subsequent lectures cover vectorial function theory, inner functions, range functions, and factoring of operator functions.
Author :
Publisher : Elsevier
ISBN 13 : 0080532802
Total Pages : 1017 pages
Book Rating : 4.0/5 (85 download)
Download or read book Handbook of the Geometry of Banach Spaces written by and published by Elsevier. This book was released on 2001-08-15 with total page 1017 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook presents an overview of most aspects of modernBanach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banachspace theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.
Author : Heydar Radjavi
Publisher : Springer Science & Business Media
ISBN 13 : 3642655742
Total Pages : 231 pages
Book Rating : 4.6/5 (426 download)
Download or read book Invariant Subspaces written by Heydar Radjavi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Vladimir G. Troitsky
Publisher :
ISBN 13 :
Total Pages : 166 pages
Book Rating : 4.:/5 (439 download)
Download or read book Invariant Subspace Problem and Spectral Properties of Bounded Linear Operators on Banach Spaces, Banach Lattices, and Topological Vector Spaces written by Vladimir G. Troitsky and published by . This book was released on 1999 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Apostol
Publisher : Birkhäuser
ISBN 13 : 3034854455
Total Pages : 222 pages
Book Rating : 4.0/5 (348 download)
Download or read book Invariant Subspaces and Other Topics written by Apostol and published by Birkhäuser. This book was released on 2013-11-21 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Yuri A. Abramovich
Publisher :
ISBN 13 : 9781470420994
Total Pages : 530 pages
Book Rating : 4.4/5 (29 download)
Download or read book An Invitation to Operator Theory written by Yuri A. Abramovich and published by . This book was released on 1900 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 recent advances in operator theory and brings together results that are spread over the vast literature. For instance, invariant subspaces of positive operators and the Daugavet equation are presented 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 important and useful role in the presentation. They help to free the proofs of the main results of technical details, which are secondary to the principal ideas, 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, and among them there are many well-known results whose proofs are not readily available elsewhere. Prerequisites are the standard introductory graduate courses in real analysis, general topology, measure theory, and functional analysis. The volume is suitable for graduate or advanced courses in operator theory, real analysis, integration theory, measure theory, function theory, and functional analysis. It will also be of great interest to researchers in mathematics, as well as in physics, economics, finance, engineering, and other related areas. The companion volume, Problems in Operator Theory, containing complete solutions to all exercises in An Invitation to Operator Theory, is available from the AMS as Volume 51 in the Graduate Studies in Mathematics series.
Author : Willi-hans Steeb
Publisher : World Scientific
ISBN 13 : 9811245746
Total Pages : 454 pages
Book Rating : 4.8/5 (112 download)
Download or read book Problems And Solutions In Banach Spaces, Hilbert Spaces, Fourier Transform, Wavelets, Generalized Functions And Quantum Mechanics written by Willi-hans Steeb and published by World Scientific. This book was released on 2022-08-23 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of problems and solutions in functional analysis with applications to quantum mechanics. Emphasis is given to Banach spaces, Hilbert spaces and generalized functions.The material of this volume is self-contained, whereby each chapter comprises an introduction with the relevant notations, definitions, and theorems. The approach in this volume is to provide students with instructive problems along with problem-solving strategies. Programming problems with solutions are also included.
