# On Uniformly Convex and Uniformly Kadec-Klee Renomings

Serdica Mathematical Journal (1995)

- Volume: 21, Issue: 1, page 1-18
- ISSN: 1310-6600

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topLancien, Gilles. "On Uniformly Convex and Uniformly Kadec-Klee Renomings." Serdica Mathematical Journal 21.1 (1995): 1-18. <http://eudml.org/doc/11654>.

@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 -

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