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

DOI: 10.2140/pjm.1982.103.17

Abstract

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

Milestones

Received: 10 July 1979

Published: 1 November 1982