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Smooth bump functions and geomentry of Banach spaces
Author(s) -
Deville R.,
Godefroy G.,
Zizler V.
Publication year - 1993
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/s0025579300007075
Subject(s) - mathematics , pointwise , smoothness , pure mathematics , moduli , banach space , type (biology) , lipschitz continuity , characterization (materials science) , mathematical analysis , ecology , physics , materials science , quantum mechanics , biology , nanotechnology
Norms with moduli of smoothness of power type are constructed on spaces with the Radon‐Nikodym property that admit pointwise Lipschitz bump functions with pointwise moduli of smoothness of power type. It is shown that no norms with pointwise moduli of rotundity of power type can exist on nonsuperreflexive spaces. A new smoothness characterization of spaces isomorphic to Hilbert spaces is given.