Locally convex spaces over non-Archimedean valued fields /
C. Perez-Garcia, W.H. Schikhof.
- Cambridge : Cambridge University Press, 2010.
- 1 online resource (xiv, 472 pages) : digital, PDF file(s).
- Cambridge studies in advanced mathematics ; 119 .
- Cambridge studies in advanced mathematics ; 119. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Ultrametrics and valuations -- Normed spaces -- Locally convex spaces -- The Hahn-Banach theorem -- The weak topology -- C-compactness -- Barrelledness and reflexivity -- Montel and nuclear spaces -- Spaces with an "orthogonal" base -- Tensor products -- Inductive limits.
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.