# Analytic Renormings of C(K) Spaces

Serdica Mathematical Journal (1996)

- Volume: 22, Issue: 1, page 25-28
- ISSN: 1310-6600

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topHájek, 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 -

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