Separably Injective Banach Spaces

  • Antonio Avilés
  • Félix Cabello Sánchez
  • Jesús M.F. Castillo
  • Manuel González
  • Yolanda  Moreno

Part of the Lecture Notes in Mathematics book series (LNM, volume 2132)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Antonio Avilés, Félix Cabello Sánchez, Jesús M. F. Castillo, Manuel González, Yolanda Moreno
    Pages 1-16
  3. Antonio Avilés, Félix Cabello Sánchez, Jesús M. F. Castillo, Manuel González, Yolanda Moreno
    Pages 17-65
  4. Antonio Avilés, Félix Cabello Sánchez, Jesús M. F. Castillo, Manuel González, Yolanda Moreno
    Pages 67-107
  5. Antonio Avilés, Félix Cabello Sánchez, Jesús M. F. Castillo, Manuel González, Yolanda Moreno
    Pages 109-134
  6. Antonio Avilés, Félix Cabello Sánchez, Jesús M. F. Castillo, Manuel González, Yolanda Moreno
    Pages 135-157
  7. Antonio Avilés, Félix Cabello Sánchez, Jesús M. F. Castillo, Manuel González, Yolanda Moreno
    Pages 159-183
  8. Back Matter
    Pages 185-220

About this book

Introduction

This monograph contains a detailed exposition of the up-to-date theory of separably injective spaces: new and old results are put into perspective with concrete examples  (such as l∞/c0 and C(K) spaces, where K is a finite height compact space or an F-space, ultrapowers of L∞ spaces and spaces of universal disposition).

It is no exaggeration to say that the theory of separably injective Banach spaces is strikingly different from that of injective spaces. For instance, separably injective Banach spaces are not necessarily isometric to, or complemented subspaces of, spaces of continuous functions on a compact space. Moreover, in contrast to the scarcity of examples and general results concerning injective spaces, we know of many different types of separably injective spaces and there is a rich theory around them. The monograph is completed with a preparatory chapter on injective spaces, a chapter on higher cardinal versions of separable injectivity and a lively discussion of open problems and further lines of research.

Keywords

46A22,46B03,46B08,46M10,46M18,26B26,54B30. Extension of operators Separably injective Banach spaces Set theoretic axioms and cardinal restrictions Spaces of universal disposition Ultraproducts of script L infinity spaces

Authors and affiliations

  • Antonio Avilés
    • 1
  • Félix Cabello Sánchez
    • 2
  • Jesús M.F. Castillo
    • 3
  • Manuel González
    • 4
  • Yolanda  Moreno
    • 5
  1. 1.Dpto. de MatemáticasUniversidad de MurciaMurciaSpain
  2. 2.Dpto. de MatemáticasUniversidad de ExtremaduraBadajozSpain
  3. 3.Dpto. de MatemáticasUniversidad de ExtremaduraBadajozSpain
  4. 4.Dpto. de MatemáticasUniversidad de CantabriaSantanderSpain
  5. 5.Dpto. de MatemáticasUniversidad de ExtremaduraCáceresSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-14741-3
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-14740-6
  • Online ISBN 978-3-319-14741-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book
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