Spectral theory of group representations and their nonstandard hull |
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Authors: | Manfred P H Wolff |
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Institution: | 1. Mathematische Fakult?t der Universit?t Tübingen, Auf der Morgenstelle 10, D-7400, Tübingen 1, FRG
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Abstract: | We construct the nonstandard hull of a not necessarily bounded strongly continuous representationU of the locally compact semigroupS on a Banach spaceE. Then we apply our results to the theory of the spectrum σ (U) ofU, mainly in cases whereS is an abelian group, e.g.S=R. First of all we obtain generalizations to the unbounded case of results known for the bounded one. Secondly we introduce
the notion of the Riesz part R σ(U) of σ(U) and characterize those representations satisfying σ(U)=R σ(U). We illustrate the theory developed so far by applications to representations on Banach lattices.
Dedicated to Prof. Dr. H. H. Schaefer on the occasion of his 60th birthday |
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