Vol. 103, No. 1, 1982

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A spectral mapping theorem for locally compact groups of operators

Claudio D’Antoni, Roberto Longo and László Zsidó

Vol. 103 (1982), No. 1, 17–24

If U is a suitably continuous representation of a locally compact abelian group G by means of isometries on a Banach space X, μ U(μ) its extension to a representation of the convolution algebra M(G) and sp(U) the spectrum of U, then the spectrum of U(μ) is not always equal to μ(sp(U)), but it is so if the continuous part of μ is absolutely continuous.

Mathematical Subject Classification 2000
Primary: 47D10, 47D10
Secondary: 22D12, 43A65
Received: 10 July 1979
Published: 1 November 1982
Claudio D’Antoni
Roberto Longo
László Zsidó