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.