On Uniformly Convex and Uniformly Kadec-Klee Renomings

@article{Lancien1995,
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.},
author = {Lancien, Gilles},
journal = {Serdica Mathematical Journal},
keywords = {Renorming; Szlenk Index; Dentability; Uniformly Convex; Kadec-Klee; Super-Reflexive; Scattered Compact; Lp Spaces; spaces; uniformly convex norms; power type modulus; super- reflexive spaces; dentability index; Szlenk index; Kadec-Klee property; weak-topology; scattered compact space},
language = {eng},
number = {1},
pages = {1-18},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On Uniformly Convex and Uniformly Kadec-Klee Renomings},
url = {http://eudml.org/doc/11654},
volume = {21},
year = {1995},
}

TY - JOUR
AU - Lancien, Gilles
TI - On Uniformly Convex and Uniformly Kadec-Klee Renomings
JO - Serdica Mathematical Journal
PY - 1995
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 21
IS - 1
SP - 1
EP - 18
AB - 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.
LA - eng
KW - Renorming; Szlenk Index; Dentability; Uniformly Convex; Kadec-Klee; Super-Reflexive; Scattered Compact; Lp Spaces; spaces; uniformly convex norms; power type modulus; super- reflexive spaces; dentability index; Szlenk index; Kadec-Klee property; weak-topology; scattered compact space
UR - http://eudml.org/doc/11654
ER -