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arXiv · 1705.05457

Spectral theory of Fourier-Stieltjes algebras

Przemysław Ohrysko·Mateusz Wasilewski
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Abstract

In this paper we start studying spectral properties of the Fourier-Stieltjes algebras, largely following Zafran's work on the algebra of measures on a locally compact group. We show that for a large class of discrete groups the Wiener-Pitt phenomenon occurs, i.e. the spectrum of an element of the Fourier-Stieltjes algebra is not captured by its range. We also investigate the notions of absolute continuity and mutual singularity in this setting; non-commutativity forces upon us two distinct versions of support of an element, indicating a crucial difference between this setup and the realm of Abelian groups. In spite of these difficulties, we also show that one can introduce and use generalised characters to prove a criterion on belonging of a multiplicative-linear functional to the Shilov boundary of the Fourier-Stieltjes algebra.

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Przemysław Ohrysko, Mateusz Wasilewski. 2017-05-15. Spectral theory of Fourier-Stieltjes algebras. https://doi.org/10.1016/j.jmaa.2018.12.040

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