[Banach] Abstract of a paper by Richard J. Smith
alspach at www.math.okstate.edu
Mon Oct 29 08:07:30 CDT 2007
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
Archive classification: math.FA
Mathematics Subject Classification: 46B03; 46B26
Remarks: A different version of this paper is to appear in J. London
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
The paper may be downloaded from the archive by web browser from
or by email in unzipped form by transmitting an empty message with
or in gzipped form by using subject line
to: math at arXiv.org.
More information about the Banach