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 in gzipped form as 0710.5396.gz with size 19kb. The corresponding postcript file has gzipped size 112kb.

Submitted from: rjs209@cam.ac.uk

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