J. Aust. Math. Soc.  78 (2005), 423-428
The spectral mapping property for p-multiplier operators on compact abelian groups

 Werner J. Ricker   Math.-Geogr. Fakultät   Katholische Universität Eichstätt-Ingolstadt   D-85072 Eichstätt   Germany  werner.ricker@ku-eichstaett.de

Abstract
Let be a compact abelian group and . It is known that the spectrum , of a Fourier -multiplier operator acting in , may fail to coincide with its natural spectrum if ; here is the dual group to and the bar denotes closure in . Criteria are presented, based on geometric, topological and/or algebraic properties of the compact set , which are sufficient to ensure that the equality holds.