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Banach Spaces of Continuous Functions as Dual Spaces

  • Book
  • © 2016

Overview

Authors:
  1. H. G. Dales

    1. Department of Mathematics and Statistics, University of Lancaster, Lancaster, United Kingdom

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  2. F.K. Dashiell, Jr.

    1. Center of Excellence in Computation Algebra, and Topology (CECAT), Chapman University, Orange, USA

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  3. A.T.-M. Lau

    1. Department of Mathematical Sciences, University of Alberta, EDMONTON, Canada

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  4. D. Strauss

    1. Department of Pure Mathematics, University of Leeds, Leeds, United Kingdom

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  • Includes a balance of well-known theorems and applications as well as new research and results
  • Provides a clear account of background information in Stonean spaces, Banach spaces, Banach lattices, Banach algebras, and measure theory
  • Discusses new approaches and syntheses of classical theorem with new examples
  • Includes supplementary material: sn.pub/extras

Part of the book series: CMS Books in Mathematics (CMSBM)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Introduction

    • H. G. Dales, F. K. Dashiell Jr., A. T.-M. Lau, D. Strauss
    Pages 1-46

  3. Banach Spaces and Banach Lattices

    • H. G. Dales, F. K. Dashiell Jr., A. T.-M. Lau, D. Strauss
    Pages 47-92

  4. Banach Algebras and C ∗-Algebras

    • H. G. Dales, F. K. Dashiell Jr., A. T.-M. Lau, D. Strauss
    Pages 93-108

  5. Measures

    • H. G. Dales, F. K. Dashiell Jr., A. T.-M. Lau, D. Strauss
    Pages 109-160

  6. Hyper-Stonean Spaces

    • H. G. Dales, F. K. Dashiell Jr., A. T.-M. Lau, D. Strauss
    Pages 161-182

  7. The Banach Space C(K)

    • H. G. Dales, F. K. Dashiell Jr., A. T.-M. Lau, D. Strauss
    Pages 183-247

  8. Back Matter

    Pages 249-277
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Keywords

About this book

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.

Reviews

“This monograph is said to be about dual C(K) spaces; but it contains a wealth of information on other related topics. … The book is very well structured and clearly written. The exposition is as self-contained as can be expected from a volume so slim.” (Timur Oikhberg, Mathematical Reviews, January, 2018)


“The material is presented in a meticulous and extremely well polished way. Readers will especially appreciate the detailed references that accompany the text. … Researchers of Banach spaces will profit a lot from this very welcome contribution to the literature.” (Dirk Werner, zbMATH 1368.46003, 2017)

Authors and Affiliations

  • Department of Mathematics and Statistics, University of Lancaster, Lancaster, United Kingdom

    H. G. Dales

  • Center of Excellence in Computation Algebra, and Topology (CECAT), Chapman University, Orange, USA

    F.K. Dashiell, Jr.

  • Department of Mathematical Sciences, University of Alberta, EDMONTON, Canada

    A.T.-M. Lau

  • Department of Pure Mathematics, University of Leeds, Leeds, United Kingdom

    D. Strauss

Bibliographic Information

  • Book Title: Banach Spaces of Continuous Functions as Dual Spaces

  • Authors: H. G. Dales, F.K. Dashiell, Jr., A.T.-M. Lau, D. Strauss

  • Series Title: CMS Books in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-32349-7

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-3-319-32347-3Published: 27 December 2016

  • Softcover ISBN: 978-3-319-81263-2Published: 07 July 2018

  • eBook ISBN: 978-3-319-32349-7Published: 13 December 2016

  • Series ISSN: 1613-5237

  • Series E-ISSN: 2197-4152

  • Edition Number: 1

  • Number of Pages: XIV, 277

  • Number of Illustrations: 6 b/w illustrations

  • Topics: Order, Lattices, Ordered Algebraic Structures, Algebraic Topology, K-Theory

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