Commutative, radical amenable Banach algebras
Studia Mathematica, Tome 140 (2000) no. 3, pp. 199-212
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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 $y_1$; then approximate $(x-y_1)/η$ within distance η by a "good" vector $y_2$, thus approximating x within distance $η^2$ by $y_1+η y_2$, 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{10_4064_sm_140_3_199_212,
author = {C. J. Read},
title = {Commutative, radical amenable {Banach} algebras},
journal = {Studia Mathematica},
pages = {199--212},
year = {2000},
volume = {140},
number = {3},
doi = {10.4064/sm-140-3-199-212},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-140-3-199-212/}
}
C. J. Read. Commutative, radical amenable Banach algebras. Studia Mathematica, Tome 140 (2000) no. 3, pp. 199-212. doi: 10.4064/sm-140-3-199-212
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