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Author : Joram Lindenstrauss
Publisher : American Mathematical Soc.
ISBN 13 : 0821812483
Total Pages : 116 pages
Book Rating : 4.8/5 (218 download)
Download or read book Extension of Compact Operators written by Joram Lindenstrauss and published by American Mathematical Soc.. This book was released on 1964 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Joram Lindenstrauss
Publisher :
ISBN 13 :
Total Pages : 1 pages
Book Rating : 4.:/5 (227 download)
Download or read book On the Extension Property for Compact Operators written by Joram Lindenstrauss and published by . This book was released on 1961 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several characterizations of Banach spaces having an extension property for compact operators are considered. In particular a characterization of such spaces is given in terms of intersection properties of their spheres similar to that given by Nachbin for P1 spaces. Our Theorem 1 extends previous results of Grothendieck. Some applications are given among them a new characterization of C(K) spaces. In this connection some problems raised by Aronszajn and Panitchpakdi and by Grothendieck and Nachbin are solved. Some results are presented concerning the C.L. spaces introduced recently by Fullerton. (Author).
Author : H. König
Publisher : Birkhäuser
ISBN 13 : 3034862784
Total Pages : 256 pages
Book Rating : 4.0/5 (348 download)
Download or read book Eigenvalue Distribution of Compact Operators written by H. König and published by Birkhäuser. This book was released on 2013-11-22 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mikhail Popov
Publisher : Walter de Gruyter
ISBN 13 : 3110263343
Total Pages : 336 pages
Book Rating : 4.1/5 (12 download)
Download or read book Narrow Operators on Function Spaces and Vector Lattices written by Mikhail Popov and published by Walter de Gruyter. This book was released on 2012-12-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most classes of operators that are not isomorphic embeddings are characterized by some kind of a “smallness” condition. Narrow operators are those operators defined on function spaces that are “small” at {-1,0,1}-valued functions, e.g. compact operators are narrow. The original motivation to consider such operators came from theory of embeddings of Banach spaces, but since then they were also applied to the study of the Daugavet property and to other geometrical problems of functional analysis. The question of when a sum of two narrow operators is narrow, has led to deep developments of the theory of narrow operators, including an extension of the notion to vector lattices and investigations of connections to regular operators. Narrow operators were a subject of numerous investigations during the last 30 years. This monograph provides a comprehensive presentation putting them in context of modern theory. It gives an in depth systematic exposition of concepts related to and influenced by narrow operators, starting from basic results and building up to most recent developments. The authors include a complete bibliography and many attractive open problems.
Author : J. Bourgain
Publisher : Springer
ISBN 13 : 3540386114
Total Pages : 147 pages
Book Rating : 4.5/5 (43 download)
Download or read book New Classes of Lp-Spaces written by J. Bourgain and published by Springer. This book was released on 2006-11-14 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this text is to present new examples of LP-spaces for 1 ≤ P ≤ ∞. This work has three reasons of interest. First, of course, it provides new LPspaces. Secondly, because certain constructions are based on new ideas and techniques with possibly other applications. Finally, especially in chapters four and five, crucial use is made of certain probabilistic results which have an independent importance.
Author : Antonio Avilés
Publisher : Springer
ISBN 13 : 3319147412
Total Pages : 236 pages
Book Rating : 4.3/5 (191 download)
Download or read book Separably Injective Banach Spaces written by Antonio Avilés and published by Springer. This book was released on 2016-03-26 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains a detailed exposition of the up-to-date theory of separably injective spaces: new and old results are put into perspective with concrete examples (such as l∞/c0 and C(K) spaces, where K is a finite height compact space or an F-space, ultrapowers of L∞ spaces and spaces of universal disposition). It is no exaggeration to say that the theory of separably injective Banach spaces is strikingly different from that of injective spaces. For instance, separably injective Banach spaces are not necessarily isometric to, or complemented subspaces of, spaces of continuous functions on a compact space. Moreover, in contrast to the scarcity of examples and general results concerning injective spaces, we know of many different types of separably injective spaces and there is a rich theory around them. The monograph is completed with a preparatory chapter on injective spaces, a chapter on higher cardinal versions of separable injectivity and a lively discussion of open problems and further lines of research.
Author : Vladimir Kadets
Publisher : Elsevier
ISBN 13 : 008047280X
Total Pages : 342 pages
Book Rating : 4.0/5 (84 download)
Download or read book Functional Analysis and its Applications written by Vladimir Kadets and published by Elsevier. This book was released on 2004-07-31 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conference took place in Lviv, Ukraine and was dedicated to a famous Polish mathematician Stefan Banach ƒ{ the most outstanding representative of the Lviv mathematical school. Banach spaces, introduced by Stefan Banach at the beginning of twentieth century, are familiar now to every mathematician. The book contains a short historical article and scientific contributions of the conference participants, mostly in the areas of functional analysis, general topology, operator theory and related topics.
Author :
Publisher : Elsevier
ISBN 13 : 0080533507
Total Pages : 873 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 2003-05-06 with total page 873 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of the Geometry of Banach Spaces
Author : Jesus Araujo-Gomez
Publisher : American Mathematical Soc.
ISBN 13 : 0821852914
Total Pages : 294 pages
Book Rating : 4.8/5 (218 download)
Download or read book Advances in Non-Archimedean Analysis written by Jesus Araujo-Gomez and published by American Mathematical Soc.. This book was released on 2011 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: These collected articles feature recent developments in various areas of non-Archimedean analysis: Hilbert and Banach spaces, finite dimensional spaces, topological vector spaces and operator theory, strict topologies, spaces of continuous functions and of strictly differentiable functions, isomorphisms between Banach functions spaces, and measure and integration.
Author : Pietro Aiena
Publisher : Springer
ISBN 13 : 3030022668
Total Pages : 552 pages
Book Rating : 4.0/5 (3 download)
Download or read book Fredholm and Local Spectral Theory II written by Pietro Aiena and published by Springer. This book was released on 2018-11-24 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph concerns the relationship between the local spectral theory and Fredholm theory of bounded linear operators acting on Banach spaces. The purpose of this book is to provide a first general treatment of the theory of operators for which Weyl-type or Browder-type theorems hold. The product of intensive research carried out over the last ten years, this book explores for the first time in a monograph form, results that were only previously available in journal papers. Written in a simple style, with sections and chapters following an easy, natural flow, it will be an invaluable resource for researchers in Operator Theory and Functional Analysis. The reader is assumed to be familiar with the basic notions of linear algebra, functional analysis and complex analysis.
Author : Walter Roth
Publisher : Springer Science & Business Media
ISBN 13 : 3540875646
Total Pages : 370 pages
Book Rating : 4.5/5 (48 download)
Download or read book Operator-Valued Measures and Integrals for Cone-Valued Functions written by Walter Roth and published by Springer Science & Business Media. This book was released on 2009-02-05 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integration theory deals with extended real-valued, vector-valued, or operator-valued measures and functions, but different approaches are used for each case. This book develops a general theory of integration that simultaneously deals with all three cases.
Author : Marian Fabian
Publisher : Springer Science & Business Media
ISBN 13 : 1475734808
Total Pages : 455 pages
Book Rating : 4.4/5 (757 download)
Download or read book Functional Analysis and Infinite-Dimensional Geometry written by Marian Fabian and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the basic principles of functional analysis and areas of Banach space theory that are close to nonlinear analysis and topology. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints.
Author : Donald I. Cartwright
Publisher : Amer Mathematical Society
ISBN 13 : 9780821818640
Total Pages : 48 pages
Book Rating : 4.8/5 (186 download)
Download or read book Extensions of Positive Operators Between Banach Lattices written by Donald I. Cartwright and published by Amer Mathematical Society. This book was released on 1975 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yuri A. Abramovich
Publisher : American Mathematical Soc.
ISBN 13 : 0821821466
Total Pages : 546 pages
Book Rating : 4.8/5 (218 download)
Download or read book An Invitation to Operator Theory written by Yuri A. Abramovich and published by American Mathematical Soc.. This book was released on 2002 with total page 546 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 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 : Javad Mashreghi
Publisher : American Mathematical Soc.
ISBN 13 : 1470410451
Total Pages : 330 pages
Book Rating : 4.4/5 (74 download)
Download or read book Invariant Subspaces of the Shift Operator written by Javad Mashreghi and published by American Mathematical Soc.. This book was released on 2015-04-23 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : H. Garth Dales
Publisher : Cambridge University Press
ISBN 13 : 9780521535847
Total Pages : 338 pages
Book Rating : 4.5/5 (358 download)
Download or read book Introduction to Banach Algebras, Operators, and Harmonic Analysis written by H. Garth Dales and published by Cambridge University Press. This book was released on 2003-11-13 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
Author : David Borthwick
Publisher : Springer Nature
ISBN 13 : 3030380025
Total Pages : 339 pages
Book Rating : 4.0/5 (33 download)
Download or read book Spectral Theory written by David Borthwick and published by Springer Nature. This book was released on 2020-03-12 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a concise introduction to spectral theory, designed for newcomers to functional analysis. Curating the content carefully, the author builds to a proof of the spectral theorem in the early part of the book. Subsequent chapters illustrate a variety of application areas, exploring key examples in detail. Readers looking to delve further into specialized topics will find ample references to classic and recent literature. Beginning with a brief introduction to functional analysis, the text focuses on unbounded operators and separable Hilbert spaces as the essential tools needed for the subsequent theory. A thorough discussion of the concepts of spectrum and resolvent follows, leading to a complete proof of the spectral theorem for unbounded self-adjoint operators. Applications of spectral theory to differential operators comprise the remaining four chapters. These chapters introduce the Dirichlet Laplacian operator, Schrödinger operators, operators on graphs, and the spectral theory of Riemannian manifolds. Spectral Theory offers a uniquely accessible introduction to ideas that invite further study in any number of different directions. A background in real and complex analysis is assumed; the author presents the requisite tools from functional analysis within the text. This introductory treatment would suit a functional analysis course intended as a pathway to linear PDE theory. Independent later chapters allow for flexibility in selecting applications to suit specific interests within a one-semester course.
