Locally Convex Spaces over Non-Archimedean Valued Fields

ISBN-13: 9780521192439 / Angielski / Twarda / 2010 / 472 str.

C Perez-Garcia

Opis

A comprehensive, self-contained treatment of non-Archimedean functional analysis, with an emphasis on locally convex space theory.

Recenzje

'The book under review is, in my opinion, the best of the existing books on the theory of non-Archimedean 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. It could be used by graduate students as well as by researchers in mathematical analysis and in other areas.' Mathematical Reviews

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.