Banach Spaces Of Continuous Functions As Dual Spaces

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Banach Spaces Of Continuous Functions As Dual Spaces

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Author : H. G. Dales
language : en
Publisher: Springer
Release Date : 2016-12-13

Banach Spaces Of Continuous Functions As Dual Spaces written by H. G. Dales and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-13 with Mathematics categories.

This book gives a coherent account of the theory of Banach spaces and Banach lattices, using the spaces C_0(K) of continuous functions on a locally compact space K as the main example. The study of C_0(K) has been an important area of functional analysis for many years. It gives several new constructions, some involving Boolean rings, of this space as well as many results on the Stonean space of Boolean rings. The book also discusses when Banach spaces of continuous functions are dual spaces and when they are bidual spaces.

Banach Spaces Of Continuous Functions

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Author : Zbigniew Semadeni
language : en
Publisher:
Release Date : 1971

Banach Spaces Of Continuous Functions written by Zbigniew Semadeni and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Banach spaces categories.

Introduction To Tensor Products Of Banach Spaces

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Author : Raymond A. Ryan
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-01-15

Introduction To Tensor Products Of Banach Spaces written by Raymond A. Ryan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-15 with Mathematics categories.

This is the first ever truly introductory text to the theory of tensor products of Banach spaces. Coverage includes a full treatment of the Grothendieck theory of tensor norms, approximation property and the Radon-Nikodym Property, Bochner and Pettis integrals. Each chapter contains worked examples and a set of exercises, and two appendices offer material on summability in Banach spaces and properties of spaces of measures.

Topics In Banach Space Theory

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Author : Fernando Albiac
language : en
Publisher: Taylor & Francis
Release Date : 2006-01-04

Topics In Banach Space Theory written by Fernando Albiac and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-04 with Mathematics categories.

This book emphasizes the isomorphic theory of Banach spaces and techniques using the unifying viewpoint of basic sequences. Its aim is to provide the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems.

Lipschitz Algebras

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Author : Nik Weaver
language : en
Publisher: World Scientific
Release Date : 1999

Lipschitz Algebras written by Nik Weaver and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

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.

The Stone Ech Compactification

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Author : R.C. Walker
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Stone Ech Compactification written by R.C. Walker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

Recent research has produced a large number of results concerning the Stone-Cech compactification or involving it in a central manner. The goal of this volume is to make many of these results easily accessible by collecting them in a single source together with the necessary introductory material. The author's interest in this area had its origin in his fascination with the classic text Rings of Continuous Functions by Leonard Gillman and Meyer Jerison. This excellent synthesis of algebra and topology appeared in 1960 and did much to draw attention to the Stone-Cech compactification {3X as a tool to investigate the relationships between a space X and the rings C(X) and C*(X) of real-valued continuous functions. Although in the approach taken here {3X is viewed as the object of study rather than as a tool, the influence of Rings of Continuous Functions is clearly evident. Three introductory chapters make the book essentially self-contained and the exposition suitable for the student who has completed a first course in topology at the graduate level. The development of the Stone Cech compactification and the more specialized topological prerequisites are presented in the first chapter. The necessary material on Boolean algebras, including the Stone Representation Theorem, is developed in Chapter 2. A very basic introduction to category theory is presented in the beginning of Chapter 10 and the remainder of the chapter is an introduction to the methods of categorical topology as it relates to the Stone-Cech compactification.

Functional Analysis

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Author : Theo Bühler
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-08

Functional Analysis written by Theo Bühler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-08 with Mathematics categories.

It begins in Chapter 1 with an introduction to the necessary foundations, including the Arzelà–Ascoli theorem, elementary Hilbert space theory, and the Baire Category Theorem. Chapter 2 develops the three fundamental principles of functional analysis (uniform boundedness, open mapping theorem, Hahn–Banach theorem) and discusses reflexive spaces and the James space. Chapter 3 introduces the weak and weak topologies and includes the theorems of Banach–Alaoglu, Banach–Dieudonné, Eberlein–Šmulyan, Kre&ibreve;n–Milman, as well as an introduction to topological vector spaces and applications to ergodic theory. Chapter 4 is devoted to Fredholm theory. It includes an introduction to the dual operator and to compact operators, and it establishes the closed image theorem. Chapter 5 deals with the spectral theory of bounded linear operators. It introduces complex Banach and Hilbert spaces, the continuous functional calculus for self-adjoint and normal operators, the Gelfand spectrum, spectral measures, cyclic vectors, and the spectral theorem. Chapter 6 introduces unbounded operators and their duals. It establishes the closed image theorem in this setting and extends the functional calculus and spectral measure to unbounded self-adjoint operators on Hilbert spaces. Chapter 7 gives an introduction to strongly continuous semigroups and their infinitesimal generators. It includes foundational results about the dual semigroup and analytic semigroups, an exposition of measurable functions with values in a Banach space, and a discussion of solutions to the inhomogeneous equation and their regularity properties. The appendix establishes the equivalence of the Lemma of Zorn and the Axiom of Choice, and it contains a proof of Tychonoff's theorem. With 10 to 20 elaborate exercises at the end of each chapter, this book can be used as a text for a one-or-two-semester course on functional analysis for beginning graduate students. Prerequisites are first-year analysis and linear algebra, as well as some foundational material from the second-year courses on point set topology, complex analysis in one variable, and measure and integration.

Perturbation Analysis Of Optimization Problems

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Author : J.Frederic Bonnans
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-22

Perturbation Analysis Of Optimization Problems written by J.Frederic Bonnans and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-22 with Mathematics categories.

The main subject of this book is perturbation analysis of continuous optimization problems. In the last two decades considerable progress has been made in that area, and it seems that it is time now to present a synthetic view of many important results that apply to various classes of problems. The model problem that is considered throughout the book is of the form (P) Min/(x) subjectto G(x) E K. xeX Here X and Y are Banach spaces, K is a closed convex subset of Y, and / : X -+ IR and G : X -+ Y are called the objective function and the constraint mapping, respectively. We also consider a parameteriZed version (P ) of the above u problem, where the objective function / (x, u) and the constraint mapping G(x, u) are parameterized by a vector u varying in a Banach space U. Our aim is to study continuity and differentiability properties of the optimal value v(u) and the set S(u) of optimal solutions of (P ) viewed as functions of the parameter vector u.

Operator Theory In Function Spaces

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Author : Kehe Zhu
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Operator Theory In Function Spaces written by Kehe Zhu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.

Fundamentals Of Nonparametric Bayesian Inference

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Author : Subhashis Ghosal
language : en
Publisher: Cambridge University Press
Release Date : 2017-06-26

Fundamentals Of Nonparametric Bayesian Inference written by Subhashis Ghosal and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-26 with Business & Economics categories.

Bayesian nonparametrics comes of age with this landmark text synthesizing theory, methodology and computation.