Introduction to Tensor Products of Banach Spaces

  • Raymond A. Ryan

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Raymond A. Ryan
    Pages 1-13
  3. Raymond A. Ryan
    Pages 15-43
  4. Raymond A. Ryan
    Pages 45-69
  5. Raymond A. Ryan
    Pages 71-92
  6. Raymond A. Ryan
    Pages 93-126
  7. Raymond A. Ryan
    Pages 127-158
  8. Raymond A. Ryan
    Pages 159-185
  9. Raymond A. Ryan
    Pages 187-199
  10. Back Matter
    Pages 201-225

About this book

Introduction

This book is intended as an introduction to the theory of tensor products of Banach spaces. The prerequisites for reading the book are a first course in Functional Analysis and in Measure Theory, as far as the Radon-Nikodym theorem. The book is entirely self-contained and two appendices give addi­ tional material on Banach Spaces and Measure Theory that may be unfamil­ iar to the beginner. No knowledge of tensor products is assumed. Our viewpoint is that tensor products are a natural and productive way to understand many of the themes of modern Banach space theory and that "tensorial thinking" yields insights into many otherwise mysterious phenom­ ena. We hope to convince the reader of the validity of this belief. We begin in Chapter 1 with a treatment of the purely algebraic theory of tensor products of vector spaces. We emphasize the use of the tensor product as a linearizing tool and we explain the use of tensor products in the duality theory of spaces of operators in finite dimensions. The ideas developed here, though simple, are fundamental for the rest of the book.

Keywords

Banach Space Tensor Products approximation property functional analysis measure

Authors and affiliations

  • Raymond A. Ryan
    • 1
  1. 1.Department of MathematicsNational University of Ireland, GalwayGalwayIreland

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-3903-4
  • Copyright Information Springer-Verlag London 2002
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-84996-872-0
  • Online ISBN 978-1-4471-3903-4
  • Series Print ISSN 1439-7382
  • About this book