Continuous dense embeddings of strong Moore algebras

Meyer, Michael J.

doi:10.1090/S0002-9939-1992-1102859-7

Continuous dense embeddings of strong Moore algebras
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by Michael J. Meyer PDF

Proc. Amer. Math. Soc. 116 (1992), 727-735 Request permission

Abstract:

We introduce the class of strong Moore Banach algebras (all topologically transitive representations of a certain type are finite dimensional) and investigate stability properties with respect to completions of such algebras in continuous submultiplicative norms. Among other things it is shown that every irreducible representation of a regular (definition below) strong Moore Banach algebra $\mathcal {A}$ extends to all Banach algebras in which $\mathcal {A}$ is continuously and densely embedded.

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