Locally convex spaces over non-Archimedean valued fields
By: C. Perez-Garcia, W.H. Schikhof.
Contributors: Schikhof, Wilhelmus Hendricus.
Series: Cambridge studies in advanced mathematics -- 119
Publisher: Cambridge University Press
Published: 2009
Place of publication: New York
Language: eng
ISBN-13: 9780521192439
Subjects: Locally convex spaces; Functional analysis
Description: "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"--Provided by publisher.

"OCALLY 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. CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS"--Provided by publisher.
Notes: Includes index.
Table of contents: title: Machine generated contents note: 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.