Analytic Renormings of C(K) Spaces

Hájek, Petr. "Analytic Renormings of C(K) Spaces." Serdica Mathematical Journal 22.1 (1996): 25-28. <http://eudml.org/doc/11625>.

@article{Hájek1996,
abstract = {The aim of our present note is to show the strength of the existence of an equivalent analytic renorming of a Banach space, even compared to C∞-Fréchet smooth renormings. It was Haydon who first showed in [8] that C(K) spaces for K countable admit an equivalent C∞-Fréchet smooth norm. Later, in [7] and [9] he introduced a large clams of tree-like (uncountable) compacts K for which C(K) admits an equivalent C∞-Fréchet smooth norm. Recently, it was shown in [3] that C(K) spaces for K countable admit an equivalent analytic norm. Our Theorem 1 shows that in the class of C(K) spaces this result is the best possible.},
author = {Hájek, Petr},
journal = {Serdica Mathematical Journal},
keywords = {Analytic Renormings; existence of an equivalent analytic renorming; -Fréchet smooth renormings},
language = {eng},
number = {1},
pages = {25-28},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Analytic Renormings of C(K) Spaces},
url = {http://eudml.org/doc/11625},
volume = {22},
year = {1996},
}

TY - JOUR
AU - Hájek, Petr
TI - Analytic Renormings of C(K) Spaces
JO - Serdica Mathematical Journal
PY - 1996
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 22
IS - 1
SP - 25
EP - 28
AB - The aim of our present note is to show the strength of the existence of an equivalent analytic renorming of a Banach space, even compared to C∞-Fréchet smooth renormings. It was Haydon who first showed in [8] that C(K) spaces for K countable admit an equivalent C∞-Fréchet smooth norm. Later, in [7] and [9] he introduced a large clams of tree-like (uncountable) compacts K for which C(K) admits an equivalent C∞-Fréchet smooth norm. Recently, it was shown in [3] that C(K) spaces for K countable admit an equivalent analytic norm. Our Theorem 1 shows that in the class of C(K) spaces this result is the best possible.
LA - eng
KW - Analytic Renormings; existence of an equivalent analytic renorming; -Fréchet smooth renormings
UR - http://eudml.org/doc/11625
ER -