Introduction to Tensor Products of Banach Spaces

Raymond A. Ryan

226 pages, parution le 27/02/2002

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Résumé

This volume provides a self-contained introduction to the theory of tensor products of Banach spaces. It is written for graduate students in analysis or for researchers in other fields who wish to become acquainted with this area. The only prerequisites are a basic knowledge of functional analysis and measure theory. Features of particular interest include:

- A full treatment of the Grothendieck theory of tensor norms;
- Coverage of the Chevet-Saphar norms and their duals, along with the associated classes of nuclear, integral and summing operators;
- Chapters on the approximation property and the Radon-Nikodým property;
- Topics such as the Bochner and Pettis integrals, the principle of local reflexivity and the Grothendieck inequality placed in a natural setting;
- The classes of operators generated by a tensor norm and connections with the theory of operator ideals.

Each chapter is accompanied by worked examples and a set of exercises, and two appendices provide essential material on summability in Banach spaces and properties of spaces of measures that may be new to the beginner.

Contents

Preface.
Notation and Terminology.

Tensor Products.
The Projective Tensor Product.
The Injective Tensor Product.
The Approximation Property.
The Radon-Nikodým Property.
The Chevet-Saphar Tensor Products.
Tensor Norms.
Operator Ideals.

Appendix A: Suggestions for Further Reading.
Appendix B: Summability in Banach Spaces.
Appendix C: Spaces of Measures.

References.
Index.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Raymond A. Ryan
Parution	27/02/2002
Nb. de pages	226
Format	16 x 24
Couverture	Broché
Poids	502g
Intérieur	Noir et Blanc
EAN13	9781852334376
ISBN13	978-1-85233-437-6