Locally Convex Spaces over Non-Archimedean Valued Fields

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.

Spis treści:
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.