Some results and criteria of existence concerning bounded approximate identities in Banach algebras are extended to the topological algebras setting. We thereby prove that the bidual of a commutative locally C*-algebra with either of the two Arens products is a unital commutative algebra, and that a quasinormable Fréchet m-convex algebra has a left (resp. right) bounded approximate identity if and only if it can be represented as an inverse limit of Banach algebras each of which has a left (resp. right) bounded approximate identity.
Publié le : 2010-12-15
Classification:
Approximate identity/units,
topological algebra,
quasinormable Fréchet m-convex algebra,
bidual of a locally convex algebra,
Arens products,
Arens regularity,
46H20,
46A20,
46H25,
46K05,
46M18,
46M40
@article{1292334069,
author = {Podara, Christina P.},
title = {Criteria of existence of bounded approximate identities in topological algebras},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {17},
number = {1},
year = {2010},
pages = { 949-960},
language = {en},
url = {http://dml.mathdoc.fr/item/1292334069}
}
Podara, Christina P. Criteria of existence of bounded approximate identities in topological algebras. Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, pp. 949-960. http://gdmltest.u-ga.fr/item/1292334069/