A new and simple proof of Schauder's theorem
Functional Analysis
2011-03-10 v4
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).
Cite
@article{arxiv.1010.1298,
title = {A new and simple proof of Schauder's theorem},
author = {Volker Runde},
journal= {arXiv preprint arXiv:1010.1298},
year = {2011}
}
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