Atlas home || Conferences | Abstracts | about Atlas

1999 Summer Conference on Topology and its Applications
August 4-7, 1999
C.W. Post Campus of Long Island University
Brookville, NY, USA

Organizers
Sheldon Rothman, Ralph Kopperman

View Abstracts
Conference Homepage

Banach spaces over nonarchimedian valued fields
by
Wim H. Schikhof
University of Nijmegen, The Netherlands

In this survey note we present the state of the art on the theory of Banach and Hilbert spaces over complete valued scalar fields that are not isomorphic to R or C. We consider `classical' theorems such as the Hahn-Banach, Closed Range, Riesz Representation, Eberlein- Smulian, and Krein-Milman theorems and discuss whether or not they remain valid in this new context; in some cases there are strong negations, in others strong improvements. Several new concepts are introduced (e.g., norm orthogonality, spherical completeness, compactoidity, modules over valuation rings) leading to results that do not have-or at least have less important-counterparts in the classical theory.

Date received: May 26, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacl-22.