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On uniformly Gâteaux differentiable norms in C ( K )
Author(s) -
Moltó A.,
Troyanski S.
Publication year - 1994
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300007348
Subject(s) - uncountable set , mathematics , differentiable function , separable space , norm (philosophy) , space (punctuation) , pure mathematics , mathematical analysis , law , political science , philosophy , countable set , linguistics
It is proved that C ( K ) has no equivalent uniformly Gâteaux differentiable norm (UGD) when K ‐is an uncountable separable scattered com¬pact space. This result is applied to obtain an example of scattered compact K such that K ′″ = ∅ and C ( K ) has no UGD renorming.