A generalization of an Ekeland-Lebourg theorem and the differentiability of distance functions
Zajíček, L.
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Zajíček, L.
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Rafał Górak (2010)
Bulletin of the Polish Academy of Sciences. Mathematics
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We show that every Lipschitz map defined on an open subset of the Banach space C(K), where K is a scattered compactum, with values in a Banach space with the Radon-Nikodym property, has a point of Fréchet differentiability. This is a strengthening of the result of Lindenstrauss and Preiss who proved that for countable compacta. As a consequence of the above and a result of Arvanitakis we prove that Lipschitz functions on certain function spaces are Gâteaux differentiable.
Yves Dutrieux (2001)
Commentationes Mathematicae Universitatis Carolinae
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We show that there is a universal control on the Szlenk index of a Lipschitz-quotient of a Banach space with countable Szlenk index. It is in particular the case when two Banach spaces are Lipschitz-homeomorphic. This provides information on the Cantor index of scattered compact sets and such that is a Lipschitz-quotient of (that is the case in particular when these two spaces are Lipschitz-homeomorphic). The proof requires tools of descriptive set theory.
P. Mankiewicz (1972)
Studia Mathematica
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Deville, Robert (2005)
Abstract and Applied Analysis
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