A new and simple proof of Schauder's theorem

Volker Runde

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arXiv · 1010.1298

A new and simple proof of Schauder's theorem

Volker Runde

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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).

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Volker Runde. 2010-10-06. A new and simple proof of Schauder's theorem. https://arxiv.org/abs/1010.1298

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