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CONTINUITY OF ACTIONS OF GROUPS AND SEMIGROUPS ON BANACH SPACES

Published online by Cambridge University Press:  30 October 2000

LAWRENCE G. BROWN
LAWRENCE G. BROWN
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA; [email protected]
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Abstract

It is shown that if a locally compact group acts isometrically on a Banach space X leaving a closed subspace M invariant, and if the induced actions on M and X/M are strongly continuous, then the action on X is strongly continuous. Since this may be of interest for one-parameter semigroups, similar results are proved for actions of suitable topological semigroups. Other generalizations are given for (suitable) non-isometric actions, non-locally compact groups, and non-Banach spaces; corollaries concerning 1-cocycles and uniformly continuous actions are given.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 62 , Issue 1 , August 2000 , pp. 107 - 116
Copyright
The London Mathematical Society 2000

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