Locally convex spaces over non archimedean valued fields 1st Edition by C Perez Garcia, WH Schikhof ISBN 0521192439 9780521192439
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ISBN 10: 0521192439
ISBN 13: 9780521192439
Author: C Perez Garcia, WH Schikhof
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.
- 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
Locally convex spaces over non archimedean valued fields 1st Table of contents:
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
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Tags: C Perez Garcia, WH Schikhof, convex spaces, archimedean