A Spectral Mapping Theorem for Representations of Compact Groups
Wolfgang Arendt
Universität Ulm, GermanyClaudio D'Antoni
Università dell’Aquila, Italy
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Abstract
Let be a strongly continuous bounded representation of a locally compact group on a Banach space . For a bounded regular Borel measure on , we denote by the operator . If is abelian, it is known that
holds if the continuous singular part of it is zero (where denotes the spectrum of the operator , sp the Arveson-spectrum of and the Fourier–Stieltjes transformation of .)
In the present article a corresponding spectral mapping theorem is proved for compact (non-abelian) groups and absolutely continuous measures. Moreover, it is shown that - in contrary to the abelian case - the spectral mapping theorem fails for purely discontinuous measures.
Cite this article
Wolfgang Arendt, Claudio D'Antoni, A Spectral Mapping Theorem for Representations of Compact Groups. Z. Anal. Anwend. 2 (1983), no. 2, pp. 127–133
DOI 10.4171/ZAA/54