Invertibility in tensor products of Q-algebras
Volume 153 / 2002
Studia Mathematica 153 (2002), 269-284 MSC: Primary 46H05. DOI: 10.4064/sm153-3-4
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.