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Title: On Uniformly Convex and Uniformly Kadec-Klee Renomings
Authors: Lancien, Gilles
Keywords: Renorming
Szlenk Index
Uniformly Convex
Scattered Compact
Lp Spaces
Issue Date: 1995
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 21, No 1, (1995), 1p-18p
Abstract: We give a new construction of uniformly convex norms with a power type modulus on super-reflexive spaces based on the notion of dentability index. Furthermore, we prove that if the Szlenk index of a Banach space is less than or equal to ω (first infinite ordinal) then there is an equivalent weak* lower semicontinuous positively homogeneous functional on X* satisfying the uniform Kadec-Klee Property for the weak*-topology (UKK*). Then we solve the UKK or UKK* renorming problems for Lp(X) spaces and C(K) spaces for K scattered compact space.
ISSN: 1310-6600
Appears in Collections:Volume 21 Number 1

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