[Banach] Abstract of a paper by Richard J. Smith
alspach at www.math.okstate.edu
Sun Nov 4 08:05:39 CST 2007
This is an announcement for the paper "Gruenhage compacta and
strictly convex dual norms" by Richard J. Smith.
Abstract: We prove that if K is a Gruenhage compact space then C(K)*
admits an equivalent, strictly convex dual norm. As a corollary,
we show that if X is a Banach space and X* is the |.|-closed linear
span of K, where K is a Gruenhage compact in the w*-topology and
|.| is equivalent to a coarser, w*-lower semicontinuous norm on X*,
then X* admits an equivalent, strictly convex dual norm. We give a
partial converse to the first result by showing that if T is a tree,
then C(T)* admits an equivalent, strictly convex dual norm if and
only if T is a Gruenhage space. Finally, we present some stability
properties satisfied by Gruenhage spaces; in particular, Gruenhage
spaces are stable under perfect images.
Archive classification: math.FA math.GN
Mathematics Subject Classification: 46B03; 46B26
The source file(s), arxiv29-10-07.tex: 67073 bytes, is(are) stored
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Submitted from: rjs209 at cam.ac.uk
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