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R-bounded Representations of L1 (G)

Research paper by Ben de Pagter, Werner J. Ricker

Indexed on: 29 Oct '07Published on: 29 Oct '07Published in: Positivity



Abstract

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.