We consider, using various tensor norms, the completed tensor product of two unital lmc algebras one of which is commutative. Our main result shows that when the tensor product of two Q-algebras is an lmc algebra, then it is a Q-algebra if and only if pointwise invertibility implies invertibility (as in the Gelfand theory). This is always the case for Fréchet algebras.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-3-4,
author = {Se\'an Dineen and Pablo Sevilla-Peris},
title = {Invertibility in tensor products of Q-algebras},
journal = {Studia Mathematica},
volume = {151},
year = {2002},
pages = {269-284},
zbl = {1033.46038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-3-4}
}
Seán Dineen; Pablo Sevilla-Peris. Invertibility in tensor products of Q-algebras. Studia Mathematica, Tome 151 (2002) pp. 269-284. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-3-4/