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© 2016

Banach Spaces of Continuous Functions as Dual Spaces

Book

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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. H. G. Dales, F. K. Dashiell Jr., A. T.-M. Lau, D. Strauss
    Pages 1-46
  3. H. G. Dales, F. K. Dashiell Jr., A. T.-M. Lau, D. Strauss
    Pages 47-92
  4. H. G. Dales, F. K. Dashiell Jr., A. T.-M. Lau, D. Strauss
    Pages 93-108
  5. H. G. Dales, F. K. Dashiell Jr., A. T.-M. Lau, D. Strauss
    Pages 109-160
  6. H. G. Dales, F. K. Dashiell Jr., A. T.-M. Lau, D. Strauss
    Pages 161-182
  7. H. G. Dales, F. K. Dashiell Jr., A. T.-M. Lau, D. Strauss
    Pages 183-247
  8. Back Matter
    Pages 249-277

About this book

Introduction

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.

Keywords

Banach Spaces Isomorphism Continuous Functions Dual Spaces Boolean Algebras Isometric Isomorphism Injective Spaces

Authors and affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of LancasterLancasterUnited Kingdom
  2. 2.Center of Excellence in Computation Algebra, and Topology (CECAT)Chapman UniversityOrangeUSA
  3. 3.Department of Mathematical SciencesUniversity of AlbertaEDMONTONCanada
  4. 4.Department of Pure MathematicsUniversity of LeedsLeedsUnited Kingdom

Bibliographic information

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)