Automatic continuity over Moore groups |
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Authors: | Volker Runde |
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Affiliation: | (1) Fachbereich 9 Mathematik, Universität des Saarlandes, Postfach 151150, 66041 Saarbrücken, Germany |
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Abstract: | LetG be a Moore group, letB be a Banach algebra, and let :L1(G)B be a homomorphism. We show that is continuous if and only if its restriction to the center ofL1(G) is continuous. As a consequence, we obtain that (i) every homomorphism fromL1(G) orC*(G) onto a dense subalgebra of a semisimple Banach algebra, and (ii) every epimorphism fromC*(G) onto a Banach algebra is automatically continuous. |
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Keywords: | 46H40 (primary) 22D15 43A20 |
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