On Relative Commutants in Tensor Products of C*-algebras.

Charles J.K. Batty

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Invertibility in tensor products of Q-algebras

Seán Dineen, Pablo Sevilla-Peris (2002)

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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.