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R-bounded Representations of L1 (G)

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We investigate R-bounded representations \(\Psi: L^{1}\left( G\right) \rightarrow {\mathcal{L}}\left( X\right) \), where X is a Banach space and G is a lca group. Observing that Ψ induces a (strongly continuous) group homomorphism \(U:G\rightarrow {\mathcal{L}}\left( X\right) \), we are then able to analyze certain classical homomorphisms U (e.g. translations in Lp (G)) from the viewpoint of R-boundedness and the theory of scalar-type spectral operators.

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Authors and Affiliations

  1. Delft Institute of Applied Mathematics, Faculty EEMCS, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands

    Ben de Pagter

  2. Math.-Geogr.Fakultät, Katholische Universität Eichstätt-Ingolstadt, D-85072, Eichstätt, Germany

    Werner J. Ricker

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  1. Ben de Pagter
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  2. Werner J. Ricker
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Correspondence to Ben de Pagter.

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Dedicated to the memory of H. H. Schaefer

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de Pagter, B., Ricker, W.J. R-bounded Representations of L1 (G). Positivity 12, 151–166 (2008). https://doi.org/10.1007/s11117-007-2130-6

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  • DOI: https://doi.org/10.1007/s11117-007-2130-6

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