Locally Convex Spaces over Non-Archimedean Valued Fields
Locally Convex Spaces over Non-Archimedean Valued Fields
$180.00
USDNon-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers are fundamental, is a fast-growing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. This book is the first to provide a comprehensive treatment of non-Archimedean locally convex spaces. The authors provide a clear exposition of the basic theory, together with complete proofs and new results from the latest research. A guide to the many illustrative examples provided, end-of-chapter notes and glossary of terms all make this book easily accessible to beginners at the graduate level, as well as specialists from a variety of disciplines.
- The first book to offer complete coverage of non-Archimedean local convexity
- Readily accessible to graduate students and interested researchers from various disciplines
- Assumes only a basic background in linear algebra, analysis and topology
Reviews & endorsements
"The book under review is, in my opinion, the best of the existing books on the theory of non-Archimedian locally convex spaces. It contains most of the known results which are published in the area. The book is self-contained and only basic knowledge of linear algebra, analysis and topology are needed to read it."
Athanasios K. Katsaras, Mathematical Reviews
Product details
February 2010Hardback
9780521192439
486 pages
234 × 155 × 27 mm
0.8kg
12 exercises
Available
Table of Contents
- Preface
- 1. Ultrametrics and valuations
- 2. Normed spaces
- 3. Locally convex spaces
- 4. The Hahn-Banach Theorem
- 5. The weak topology
- 6. C-compactness
- 7. Barrelledness and reflexivity
- 8. Montel and nuclear spaces
- 9. Spaces with an 'orthogonal' base
- 10. Tensor products
- 11. Inductive limits
- A. Glossary of terms
- B. Guide to the examples
- Bibliography
- Notations
- Index.
