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 phenomena. 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.
1101006860
Introduction to Tensor Products of Banach Spaces
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 phenomena. 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.
159.99
In Stock
5
1
Introduction to Tensor Products of Banach Spaces
226
Introduction to Tensor Products of Banach Spaces
226Paperback(Softcover reprint of hardcover 1st ed. 2002)
$159.99
159.99
In Stock
Product Details
| ISBN-13: | 9781849968720 |
|---|---|
| Publisher: | Springer London |
| Publication date: | 12/10/2010 |
| Series: | Springer Monographs in Mathematics |
| Edition description: | Softcover reprint of hardcover 1st ed. 2002 |
| Pages: | 226 |
| Product dimensions: | 7.01(w) x 10.00(h) x 0.02(d) |
From the B&N Reads Blog