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Continuous dense embeddings of strong Moore algebras

Author: Michael J. Meyer
Journal: Proc. Amer. Math. Soc. 116 (1992), 727-735
MSC: Primary 46H15; Secondary 46H20
MathSciNet review: 1102859
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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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Keywords: Extension of finite dimensional representations
Article copyright: © Copyright 1992 American Mathematical Society

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