Locally Convex Spaces over Non-Archimedean Valued Fields

A comprehensive, self-contained treatment of non-Archimedean functional analysis, with an emphasis on locally convex space theory.

C. Perez-Garcia (Author), W. H. Schikhof (Author)

9780521192439, Cambridge University Press

Hardback, published 7 January 2010

486 pages, 12 exercises
23.4 x 15.5 x 2.7 cm, 0.8 kg

'The book under review is, in my opinion, the best of the existing books on the theory of non-Archimedean 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. It could be used by graduate students as well as by researchers in mathematical analysis and in other areas.' Mathematical Reviews

Non-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.

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.

Subject Areas: Functional analysis & transforms [PBKF]