Geodesic
Commutative, radical amenable Banach algebras
Studia Mathematica, Tome 140 (2000) no. 3, pp. 199-212

Voir la notice de l'article provenant de 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.
DOI : 10.4064/sm-140-3-199-212
Keywords: adical, Banach algebra, amenable, nilpotent

C. J. Read 1

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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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