Introduction to Tensor Products of Banach Spaces [Hardcover]

This is the first ever truly introductory text to the theory of tensor products of Banach spaces. Coverage includes a full treatment of the Grothendieck theory of tensor norms, approximation property and the Radon-Nikodym Property, Bochner and Pettis integrals. Each chapter contains worked examples and a set of exercises, and two appendices offer material on summability in Banach spaces and properties of spaces of measures.

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.1 Tensor Products.- 2 The Projective Tensor Product.- 3 The Injective Tensor Product.- 4 The Approximation Property.- 5 The Radon-Nikod?m Property.- 6 The Chevet-Saphar Tensor Products.- 7 Tensor Norms.- 8 Operator Ideals.- A Suggestions for Further Reading.- B Summability in Banach Spaces.- C Spaces of Measures.- References.

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