Locally convex spaces over non-Archimedean valued fields
著者
書誌事項
Locally convex spaces over non-Archimedean valued fields
（Cambridge studies in advanced mathematics, 119）
Cambridge University Press, 2010
- : hardback
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注記
Includes bibliographical references (p. 457-467) and index
内容説明・目次
内容説明
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.
目次
- 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.
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