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Title: Analytic Renormings of C(K) Spaces
Authors: Hájek, Petr
Keywords: Analytic Renormings
Issue Date: 1996
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 22, No 1, (1996), 25p-28p
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.
ISSN: 1310-6600
Appears in Collections:Volume 22 Number 1

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