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Simple motion systems and Banach spaces associated to uniformly bounded representations

Published online by Cambridge University Press:  01 July 1999

MATTHIAS MAYER  and
CHRISTIAN SALLER
MATTHIAS MAYER
Affiliation:
Technische Universität München, Zentrum Mathematik, D-80333 München, Germany; e-mail: [email protected] e-mail: [email protected]
CHRISTIAN SALLER
Affiliation:
Technische Universität München, Zentrum Mathematik, D-80333 München, Germany; e-mail: [email protected] e-mail: [email protected]
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Abstract

Given a uniformly bounded representation of a locally compact group, we consider the closed circled convex hull K of the orbit of a vector. We call K a simple motion system (SMS) and endow its linear hull with the Minkowski functional of K. The representation theory on these ‘SMS-spaces’ is discussed, in particular for C0-representations, for irreducible representations of connected groups and for integrable representations. As an application we give a criterion for the decomposibility of representations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 127 , Issue 1 , July 1999 , pp. 133 - 147
Copyright
The Cambridge Philosophical Society 1999

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