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History Of Banach Spaces And Linear Operators
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Book Synopsis History of Banach Spaces and Linear Operators by : Albrecht Pietsch
Download or read book History of Banach Spaces and Linear Operators written by Albrecht Pietsch and published by Springer Science & Business Media. This book was released on 2007-12-31 with total page 855 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.
Book Synopsis History of Banach Spaces and Linear Operators by : Albrecht Pietsch
Download or read book History of Banach Spaces and Linear Operators written by Albrecht Pietsch and published by . This book was released on 2003 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Factorization of Linear Operators and Geometry of Banach Spaces by : Gilles Pisier
Download or read book Factorization of Linear Operators and Geometry of Banach Spaces written by Gilles Pisier and published by American Mathematical Soc.. This book was released on 1986 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the considerable progress made in Banach space theory as a result of Grothendieck's fundamental paper ""Resume De la Theorie Metrique des Produits Tensoriels Topologiques"". The author examines the central question of which Banach spaces $X$ and $Y$ have the property that every bounded operator from $X$ to $Y$ factors through a Hilbert space, in particular when the operators are defined on a Banach lattice, a $C^*$-algebra or the disc algebra and $H^\infty$. He reviews the six problems posed at the end of Grothendieck's paper, which have now all been solved (except perhaps the exact value of Grothendieck's constant), and includes the various results which led to their solution. The last chapter contains the author's construction of several Banach spaces such that the injective and projective tensor products coincide; this gives a negative solution to Grothendieck's sixth problem.Although the book is aimed at mathematicians working in functional analysis, harmonic analysis and operator algebras, its detailed and self-contained treatment makes the material accessible to nonspecialists with a grounding in basic functional analysis. In fact, the author is particularly concerned to develop very recent results in the geometry of Banach spaces in a form that emphasizes how they may be applied in other fields, such as harmonic analysis and $C^*$-algebras.
Book Synopsis Trends in Banach Spaces and Operator Theory by : Anna Kamińska
Download or read book Trends in Banach Spaces and Operator Theory written by Anna Kamińska and published by American Mathematical Soc.. This book was released on 2003 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains proceedings of the conference on Trends in Banach Spaces and Operator Theory, which was devoted to recent advances in theories of Banach spaces and linear operators. Included in the volume are 25 papers, some of which are expository, while others present new results. The articles address the following topics: history of the famous James' theorem on reflexivity, projective tensor products, construction of noncommutative $L p$-spaces via interpolation, Banach spaces with abundance of nontrivial operators, Banach spaces with small spaces of operators, convex geometry of Coxeter-invariant polyhedra, uniqueness of unconditional bases in quasi-Banach spaces, dynamics of cohyponormal operators, and Fourier algebras for locally compact groupoids. The book is suitable for graduate students and research mathematicians interested in Banach spaces and operator theory and their applications.
Book Synopsis Theory of Linear Operations by : S. Banach
Download or read book Theory of Linear Operations written by S. Banach and published by Elsevier. This book was released on 1987-03-01 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra. The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series. A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'') complements this important monograph.
Book Synopsis Introduction to the Analysis of Normed Linear Spaces by : J. R. Giles
Download or read book Introduction to the Analysis of Normed Linear Spaces written by J. R. Giles and published by Cambridge University Press. This book was released on 2000-03-13 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a basic course in functional analysis for senior undergraduate and beginning postgraduate students. The reader need only be familiarity with elementary real and complex analysis, linear algebra and have studied a course in the analysis of metric spaces; knowledge of integration theory or general topology is not required. The text concerns the structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. The implications of the general theory are illustrated with a great variety of example spaces.
Book Synopsis Basic Classes of Linear Operators by : Israel Gohberg
Download or read book Basic Classes of Linear Operators written by Israel Gohberg and published by Springer Science & Business Media. This book was released on 2003-10-24 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive graduate textbook that introduces functional analysis with an emphasis on the theory of linear operators and its application to differential equations, integral equations, infinite systems of linear equations, approximation theory, and numerical analysis. As a textbook designed for senior undergraduate and graduate students, it begins with the geometry of Hilbert spaces and proceeds to the theory of linear operators on these spaces including Banach spaces. Presented as a natural continuation of linear algebra, the book provides a firm foundation in operator theory which is an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.
Book Synopsis Interpolation of Linear Operators by : S. G. Krein
Download or read book Interpolation of Linear Operators written by S. G. Krein and published by American Mathematical Soc.. This book was released on 2002-10-21 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory of Linear Operations by : Stefan Banach
Download or read book Theory of Linear Operations written by Stefan Banach and published by Dover Books on Mathematics. This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by the founder of functional analysis, this is the first text on linear operator theory. Additional topics include the calculus of variations and theory of integral equations. 1987 edition.
Book Synopsis Representations of Linear Operators Between Banach Spaces by : David E. Edmunds
Download or read book Representations of Linear Operators Between Banach Spaces written by David E. Edmunds and published by Springer Science & Business Media. This book was released on 2013-09-04 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with the representation in series form of compact linear operators acting between Banach spaces, and provides an analogue of the classical Hilbert space results of this nature that have their roots in the work of D. Hilbert, F. Riesz and E. Schmidt. The representation involves a recursively obtained sequence of points on the unit sphere of the initial space and a corresponding sequence of positive numbers that correspond to the eigenvectors and eigenvalues of the map in the Hilbert space case. The lack of orthogonality is partially compensated by the systematic use of polar sets. There are applications to the p-Laplacian and similar nonlinear partial differential equations. Preliminary material is presented in the first chapter, the main results being established in Chapter 2. The final chapter is devoted to the problems encountered when trying to represent non-compact maps.
Book Synopsis The Asymptotic Behaviour of Semigroups of Linear Operators by : Jan van Neerven
Download or read book The Asymptotic Behaviour of Semigroups of Linear Operators written by Jan van Neerven and published by Birkhäuser. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic account of the theory of asymptotic behaviour of semigroups of linear operators acting in a Banach space. The focus is on the relationship between asymptotic behaviour of the semigroup and spectral properties of its infinitesimal generator. The most recent developments in the field are included, such as the Arendt-Batty-Lyubich-Vu theorem, the spectral mapp- ing theorem of Latushkin and Montgomery-Smith, Weis's theorem on stability of positive semigroup in Lp-spaces, the stability theorem for semigroups whose resolvent is bounded in a half-plane, and a systematic theory of individual stability. Addressed to researchers and graduate students with interest in the fields of operator semigroups and evolution equations, this book is self-contained and provides complete proofs.
Book Synopsis Calkin Algebras and Algebras of Operators on Banach SPates by : Caradus
Download or read book Calkin Algebras and Algebras of Operators on Banach SPates written by Caradus and published by Routledge. This book was released on 2017-10-19 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the appearance of Banach algebra theory, the interaction between the theories ofBanach algebras with involution and that of bounded linear operators on a Hilbert space hasbeen extensively developed. The connections of Banach algebras with the theory ofbounded linear operators on a Hilbert space have also evolved, and Calkin Algebras andAlgebras of Operators on Banach Spaces provides an introduction to this set of ideas.The book begins with a treatment of the classical Riesz-Schauder theory which takesadvantage of the most recent developments-some of this material appears here for the firsttime. Although the reader should be familiar with the basics of functional analysis, anintroductory chapter on Banach algebras has been included. Other topics dealt with includeFredholm operators, semi-Fredholm operators, Riesz operators. and Calkin algebras.This volume will be of direct interest to both graduate students and research mathematicians.
Book Synopsis An Introduction to Banach Space Theory by : Robert E. Megginson
Download or read book An Introduction to Banach Space Theory written by Robert E. Megginson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.
Book Synopsis Traces and Determinants of Linear Operators by : Israel Gohberg
Download or read book Traces and Determinants of Linear Operators written by Israel Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to a theory of traces and determinants on embedded algebras of linear operators, where the trace and determinant are extended from finite rank operators by a limit process. The self-contained material should appeal to a wide group of mathematicians and engineers, and is suitable for teaching.
Book Synopsis Classes of Linear Operators by : Israel Gohberg
Download or read book Classes of Linear Operators written by Israel Gohberg and published by Birkhauser. This book was released on 1990 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Operators and Differential Equations in Banach Spaces by : Robert H. Martin
Download or read book Nonlinear Operators and Differential Equations in Banach Spaces written by Robert H. Martin and published by . This book was released on 1987 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Banach Spaces of Analytic Functions and Absolutely Summing Operators by :
Download or read book Banach Spaces of Analytic Functions and Absolutely Summing Operators written by and published by American Mathematical Soc.. This book was released on 1977-12-31 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys results concerning bases and various approximation properties in the classical spaces of analytical functions. It contains extensive bibliographical comments.
