Representation Theorems on Banach Function Spaces PDF Download

Author: Neil E. Gretsky
Publisher: American Mathematical Soc.
ISBN: 082181284X
Category : Banach spaces
Languages : en
Pages : 60

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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: Jaroslav Lukeš
Publisher: Walter de Gruyter
ISBN: 3110203200
Category : Mathematics
Languages : en
Pages : 732

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Book Description
This monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet's theory of function spaces with a link to compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book form for the first time. The text is self-contained and covers a wide range of applications. From the contents: Geometry of convex sets Choquet theory of function spaces Affine functions on compact convex sets Perfect classes of functions and representation of affine functions Simplicial function spaces Choquet's theory of function cones Topologies on boundaries Several results on function spaces and compact convex sets Continuous and measurable selectors Construction of function spaces Function spaces in potential theory and Dirichlet problem Applications

Author: Albrecht Pietsch
Publisher: Springer Science & Business Media
ISBN: 0817645969
Category : Mathematics
Languages : en
Pages : 877

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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.

Author: J. Lindenstrauss
Publisher: Springer Science & Business Media
ISBN: 3662353474
Category : Mathematics
Languages : en
Pages : 253

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Author: W. A. J. Luxemburg
Publisher:
ISBN:
Category : Banach spaces
Languages : en
Pages : 126

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Author: Kenneth Hoffman
Publisher: Courier Corporation
ISBN: 048614996X
Category : Mathematics
Languages : en
Pages : 227

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Book Description
A classic of pure mathematics, this advanced graduate-level text explores the intersection of functional analysis and analytic function theory. Close in spirit to abstract harmonic analysis, it is confined to Banach spaces of analytic functions in the unit disc. The author devotes the first four chapters to proofs of classical theorems on boundary values and boundary integral representations of analytic functions in the unit disc, including generalizations to Dirichlet algebras. The fifth chapter contains the factorization theory of Hp functions, a discussion of some partial extensions of the factorization, and a brief description of the classical approach to the theorems of the first five chapters. The remainder of the book addresses the structure of various Banach spaces and Banach algebras of analytic functions in the unit disc. Enhanced with 100 challenging exercises, a bibliography, and an index, this text belongs in the libraries of students, professional mathematicians, as well as anyone interested in a rigorous, high-level treatment of this topic.

Author: Krzysztof Jarov
Publisher: CRC Press
ISBN: 1000147932
Category : Mathematics
Languages : en
Pages : 450

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This book is based on the conference on Function Spaces held at Southern Illinois University at Edwardsville, in April, 1990. It is designed to cover a wide range of topics, including spaces of analytic functions, isometries of function spaces, geometry of Banach spaces, and Banach algebras.

Author: Robert E. Megginson
Publisher: Springer Science & Business Media
ISBN: 1461206030
Category : Mathematics
Languages : en
Pages : 613

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Book Description
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.

Author: María Aránzazu Juan Blanco
Publisher: LAP Lambert Academic Publishing
ISBN: 9783848409976
Category :
Languages : en
Pages : 84

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Book Description
The space of integrable functions with respect to a vector measure finds applications in important problems as the integral representation and the study of the optimal domain of linear operators or the representation of abstract Banach lattices as spaces of functions. Classical vector measures are defined on a -algebra and with values in a Banach space. However, this framework is not enough for applications to operators on spaces which do not contain the characteristic functions of sets or Banach lattices without weak unit. These cases require the vector measure to be defined on a -ring. In this work we are mainly interested in providing the properties which guarantee the representation of a Banach lattice by means of an space of integrable functions with respect to a vector measure on a -ring. The analytic properties of a vector measure are directly related to the lattice properties of the space L1. It will be also the aim of this work to study the effect of certain properties of the vector measure on the lattice structure of the space L1w. We also study the spaces Lp, Lpw for a vector measure on a -ring and the corresponding representation theorems by means of these spaces.