# R-bounded Representations of L 1 (G)

R-bounded Representations of L 1 (G) 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 L p (G)) from the viewpoint of R-boundedness and the theory of scalar-type spectral operators. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# R-bounded Representations of L 1 (G)

, Volume 12 (1) – Oct 29, 2007
16 pages

/lp/springer_journal/r-bounded-representations-of-l-1-g-7ZL0r4cFeQ
Publisher
Springer Journals
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-007-2130-6
Publisher site
See Article on Publisher Site

### 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 L p (G)) from the viewpoint of R-boundedness and the theory of scalar-type spectral operators.

### Journal

PositivitySpringer Journals

Published: Oct 29, 2007

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