Extension of Compact Operators PDF Download

Author: Joram Lindenstrauss
Publisher: American Mathematical Soc.
ISBN: 0821812483
Category : Banach spaces
Languages : en
Pages : 116

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Publisher: Elsevier
ISBN: 0080533507
Category : Mathematics
Languages : en
Pages : 873

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Handbook of the Geometry of Banach Spaces

Author: Donald I. Cartwright
Publisher: Amer Mathematical Society
ISBN: 9780821818640
Category : Mathematics
Languages : en
Pages : 48

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Book Description

Author: William B. Johnson
Publisher: Elsevier
ISBN: 9780444513052
Category : Banach spaces
Languages : en
Pages : 880

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Book Description
The Handbook presents an overview of most aspects of modern Banach 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 Banach space 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: S. Okada
Publisher: Springer Science & Business Media
ISBN: 3764386487
Category : Mathematics
Languages : en
Pages : 406

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Book Description
This book deals with the analysis of linear operators from a quasi-Banach function space into a Banach space. The central theme is to extend the operator to as large a (function) space as possible, its optimal domain, and to take advantage of this in analyzing the original operator. Most of the material appears in print for the first time. The book has an interdisciplinary character and is aimed at graduates, postgraduates, and researchers in modern operator theory.

Author: Nik Weaver
Publisher: World Scientific
ISBN: 9789810238735
Category : Mathematics
Languages : en
Pages : 242

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Book Description
The Lipschitz algebras Lp(M), for M a complete metric space, are quite analogous to the spaces C(omega) and Linfinity(X), for omega a compact Hausdorff space and X a sigma-finite measure space. Although the Lipschitz algebras have not been studied as thoroughly as these better-known cousins, it is becoming increasingly clear that they play a fundamental role in functional analysis, and are also useful in many applications, especially in the direction of metric geometry. This book gives a comprehensive treatment of (what is currently known about) the beautiful theory of these algebras.

Author: Joseph A. Ball
Publisher: Springer Science & Business Media
ISBN: 3034601581
Category : Mathematics
Languages : en
Pages : 624

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Book Description
This is the first volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.

Author: Akhmerov
Publisher: Birkhäuser
ISBN: 3034857276
Category : Science
Languages : en
Pages : 260

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Book Description
A condensing (or densifying) operator is a mapping under which the image of any set is in a certain sense more compact than the set itself. The degree of noncompactness of a set is measured by means of functions called measures of noncompactness. The contractive maps and the compact maps [i.e., in this Introduction, the maps that send any bounded set into a relatively compact one; in the main text the term "compact" will be reserved for the operators that, in addition to having this property, are continuous, i.e., in the authors' terminology, for the completely continuous operators] are condensing. For contractive maps one can take as measure of noncompactness the diameter of a set, while for compact maps can take the indicator function of a family of non-relatively com pact sets. The operators of the form F( x) = G( x, x), where G is contractive in the first argument and compact in the second, are also condensing with respect to some natural measures of noncompactness. The linear condensing operators are characterized by the fact that almost all of their spectrum is included in a disc of radius smaller than one. The examples given above show that condensing operators are a sufficiently typical phenomenon in various applications of functional analysis, for example, in the theory of differential and integral equations. As is turns out, the condensing operators have properties similar to the compact ones.

Author: Richard V. Kadison
Publisher: American Mathematical Soc.
ISBN: 0821814419
Category : Mathematics
Languages : en
Pages : 654

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Book Description

Author: Jesus M. F. Castillo
Publisher: Cambridge University Press
ISBN: 0521685680
Category : Mathematics
Languages : en
Pages : 371

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Book Description
A comprehensive overview of modern Banach space theory.