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Lipschitz Smooth Points of Convex Functions and Isomorphic Characterizations of Hilbert Spaces
Author(s) -
Fabian M.
Publication year - 1985
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-51.1.113
Subject(s) - mathematics , lipschitz continuity , pure mathematics , regular polygon , hilbert space , convex function , geometry
Banach spaces such that each convex continuous function has a dense set of Lipschitz smooth points are studied. For instance, a ‘Lipschitz’ analogy of a theorem of Ekeland and Lebourg is proved. An isomorphic characterization of Hilbert space is given, improving a result of Whitfield, Zizler, and the author.
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