[Banach] Abstract of a paper by Richard J. Smith

[Dale Alspach]

This is an announcement for the paper "Trees, linear orders and
G\^ateaux smooth norms" by Richard J. Smith.


Abstract: We introduce a linearly ordered set Z and use it to prove
a necessity condition for the existence of a G\^ateaux smooth norm
on C(T), where T is a tree. This criterion is directly analogous
to the corresponding equivalent condition for Fr\'echet smooth
norms. In addition, we prove that if C(T) admits a G\^ateaux smooth
lattice norm then it also admits a lattice norm with strictly convex
dual norm.

Archive classification: math.FA

Mathematics Subject Classification: 46B03; 46B26

Remarks: A different version of this paper is to appear in J. London
Math. Soc

The source file(s), arxiv12-10-07.tex: 60917 bytes, is(are) stored
in gzipped form as 0710.4230.gz with size 18kb. The corresponding
postcript file has gzipped size 102kb.

Submitted from: rjs209 at cam.ac.uk

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 http://front.math.ucdavis.edu/0710.4230

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 http://arXiv.org/abs/0710.4230

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