Locally Convex Spaces over Non-Archimedean Valued Fields

by C. Perez-Garcia, W. H. Schikhof

Overview

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.

Product Details

ISBN-13:	9780521192439
Publisher:	Cambridge University Press
Publication date:	01/07/2010
Series:	Cambridge Studies in Advanced Mathematics , #119
Pages:	486
Product dimensions:	6.00(w) x 9.00(h) x 1.20(d)

About the Author

C. Perez-Garcia is Professor in the Department of Mathematics, Statistics and Computation at the University of Cantabria, Spain.

W. H. Schikhof worked as a Professor at Radboud University Nijmegen, Netherlands for forty years. He has since retired but is still active in mathematical research.

Table of Contents

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.

Editorial Reviews

"The book under review is, in my opinion, the best of the existing books on the theory of non-Archimedian 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."
Athanasios K. Katsaras, Mathematical Reviews

From the Publisher