Nonarchimedean Functional Analysis

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Beschreibung

This book grew out of a course which I gave during the winter term 1997/98 at the Universitat Munster. The course covered the material which here is presented in the first three chapters. The fourth more advanced chapter was added to give the reader a rather complete tour through all the important aspects of the theory of locally convex vector spaces over nonarchimedean fields. There is one serious restriction, though, which seemed inevitable to me in the interest of a clear presentation. In its deeper aspects the theory depends very much on the field being spherically complete or not. To give a drastic example, if the field is not spherically complete then there exist nonzero locally convex vector spaces which do not have a single nonzero continuous linear form. Although much progress has been made to overcome this problem a really nice and complete theory which to a large extent is analogous to classical functional analysis can only exist over spherically complete field8. I therefore allowed myself to restrict to this case whenever a conceptual clarity resulted. Although I hope that thi8 text will also be useful to the experts as a reference my own motivation for giving that course and writing this book was different. I had the reader in mind who wants to use locally convex vector spaces in the applications and needs a text to quickly gra8p this theory.

Zusammenfassung

Covers all the important aspects of the theory of locally convex vector spaces over nonarchimedean fields

Gives the foundations of the theory and also develops the more advanced topics

Concise introduction for the researcher and the graduate student who want to apply this theory

Includes supplementary material: [...]

Inhaltsverzeichnis

I. Foundations.- Nonarchimedean Fields; Seminorms; Normed Vector Spaces; Locally Convex Vector Spaces; Constructions and Examples; Spaces of Continuous Linear Maps; Completeness; Fréchet Spaces; the Dual Space. - II. The Structure of Banach Spaces.- Structure theorems; Non-Reflexivity.- III. Duality Theory.- C-Compact and Compactoid Submodules; Polarity; Admissible Topologies; Reflexivity; Compact Limits.- IV. Nuclear Maps and Spaces.- Topological Tensor Products; Completely Continuous Maps; Nuclear Spaces; Nuclear Maps; Traces; Fredholm Theory.- References.- Index, Notations.

Details

Erscheinungsjahr:	2001
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Springer Monographs in Mathematics
Inhalt:	vii 156 S.
ISBN-13:	9783540425335
ISBN-10:	3540425330
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Schneider, Peter
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg Springer Monographs in Mathematics
Maße:	241 x 160 x 15 mm
Von/Mit:	Peter Schneider
Erscheinungsdatum:	20.11.2001
Gewicht:	0,43 kg

Artikel-ID: 104625563