There has been a considerable search for radical, amenable Banach algebras. Noncommutative examples were finally found by Volker Runde [R]; here we present the first commutative examples. Centrally placed within the construction, the reader may be pleased to notice a reprise of the undergraduate argument that shows that a normed space with totally bounded unit ball is finite-dimensional; we use the same idea (approximate the norm 1 vector x within distance η by a “good” vector ; then approximate within distance η by a “good” vector , thus approximating x within distance by , and so on) to go from η=9/10 in Lemma 1.5 to arbitrarily small η in Lemma 2.1. This is not an arbitrary decision on the part of the author; it really is forced on him by the nature of the construction, see e.g. (6.1) for a place where η small at the start will not do.
@article{bwmeta1.element.bwnjournal-article-smv140i3p199bwm,
author = {C. Read},
title = {Commutative, radical amenable Banach algebras},
journal = {Studia Mathematica},
volume = {141},
year = {2000},
pages = {199-212},
zbl = {0972.46031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv140i3p199bwm}
}
Read, C. Commutative, radical amenable Banach algebras. Studia Mathematica, Tome 141 (2000) pp. 199-212. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv140i3p199bwm/
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