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Filter products of C0-semigroups and ultraproduct representations for Lie groups |
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| Authors: | Pierre-Alain Cherix Michael Cowling |
| Affiliation: | a Section de Mathématiques, Université de Genève, 2-4, Rue de Lièvre, 1211 Geneva 24, Switzerland b School of Mathematics, The University of New South Wales, UNSW Sydney, NSW 2052, Australia c Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, MO 65409, USA |
| Abstract: | We provide a new approach to filter products of C0-semigroups and prove a spectral theorem for the generator and its filter product. In a similar fashion, we construct ultraproducts of strongly continuous unitary representations of locally compact groups and study spectral theoretic connections between the representations and their ultraproducts. In the case of Lie groups, our investigations are extended to the infinitesimal representation. |
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