This is an announcement for the paper "A new and simple proof of Schauder's theorem" by Volker Runde.

Abstract: Schauder's theorem asserts that a bounded linear operator between Banach spaces is compact if ad only if its adjoint is. We give a new proof of this result, which is both short and completely elementary in the sense that it does not depend on anything beyond basic functional analysis, i.e., the Hahn--Banach theorem and some of its consequences; in particular, we avoid the Arzela--Ascoli theorem (and any kind of related diagonal argument).

Archive classification: math.FA

Submitted from: vrunde@ualberta.ca

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1010.1298

or

http://arXiv.org/abs/1010.1298