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On The Invariant Subspace Problem
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Book Synopsis Modern Approaches to the Invariant-Subspace Problem by : Isabelle Chalendar
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.
Book Synopsis Fixed Point Theorems and Applications by : Vittorino Pata
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.
Book Synopsis Introduction to Operator Theory and Invariant Subspaces by : B. Beauzamy
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.
Book Synopsis On the Invariant Subspace Problem by : Damian Betebenner
Download or read book On the Invariant Subspace Problem written by Damian Betebenner and published by . This book was released on 1996 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Functional Analysis by : Peter D. Lax
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.
Book Synopsis Invariant Subspaces by : Heydar Radjavi
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.
Book Synopsis Invariant Subspaces of Matrices with Applications by : Israel Gohberg
Download or read book Invariant Subspaces of Matrices with Applications written by Israel Gohberg and published by SIAM. This book was released on 2006-03-01 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on Invariant Subspaces by : Henry Helson
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.
Book Synopsis Invariant Subspaces and Allied Topics by : Bhuri Singh Yadav
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:
Book Synopsis On the Invariant Subspace Problem for Banach Spaces by : Per Enflo
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:
Book Synopsis Modern Approaches to the Invariant-Subspace Problem by : Isabelle Chalendar
Download or read book Modern Approaches to the Invariant-Subspace Problem written by Isabelle Chalendar and published by . This book was released on 2011 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents work on the invariant subspace problem, a major unsolved problem in operator theory.
Book Synopsis Facets of the Invariant Subspace Problem in Banach and Hilbert Spaces by : Damian Betebenner
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:
Book Synopsis Elementary Functional Analysis by : Barbara MacCluer
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.
Book Synopsis The Invariant Subspace Problem by : Barbara Ellen Coulter
Download or read book The Invariant Subspace Problem written by Barbara Ellen Coulter and published by . This book was released on 1979 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Invariant Subspace Theorems by : R. Tunç Misirlioglu
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.
Book Synopsis The Invariant Subspace Problem by : Johathan A. Noel
Download or read book The Invariant Subspace Problem written by Johathan A. Noel and published by . This book was released on 2011 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Invariant Subspaces 1969 by : Paul Richard Halmos
Download or read book Invariant Subspaces 1969 written by Paul Richard Halmos and published by . This book was released on 1969 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
