Locally Convex Spaces over Non-Archimedean Valued Fields

Informationen zum Autor C. Perez-Garcia is Professor in the Department of Mathematics, Statistics and Computation at the University of Cantabria, Spain. Klappentext A comprehensive, self-contained treatment of non-Archimedean functional analysis, with an emphasis on locally convex space theory. Zusammenfassung This self-contained treatment of the theory of non-Archimedean locally convex spaces provides a clear exposition of the theory! together with complete proofs. A guide to examples and glossary of terms make the book easily accessible to beginners at the graduate level as well as specialists from various disciplines. Inhaltsverzeichnis 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.

Klappentext

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

Zusammenfassung
This self-contained treatment of the theory of non-Archimedean locally convex spaces provides a clear exposition of the theory, together with complete proofs. A guide to examples and glossary of terms make the book easily accessible to beginners at the graduate level as well as specialists from various disciplines.

Inhalt

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.