Locally 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

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:

1 Ultrametrics and valuations 1

2 Normed spaces 14

3 Locally convex spaces 81

4 The Hahn-Banach Theorem 170

5 The weak topology 210

6 C-compactness 244

7 Barrelledness and reflexivity 254

8 Montel and nuclear spaces 301

9 Spaces with an "orthogonal" base 337

10 Tensor products 373

11 Inductive limits 409

Appendix A Glossary of terms 442

Appendix B Guide to the examples 451

Notation 453

References 457

Index 468

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Locally Convex Spaces over Non-Archimedean Valued Fields