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The Spectral Radius Formula for Fourier–Stieltjes Algebras

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  22 July 2019

Przemysław Ohrysko  and
Maria Roginskaya
Przemysław Ohrysko
Affiliation:
Chalmers University of Technology and the University of Gothenburg Email: p.ohrysko@gmail.commaria.roginskaya@chalmers.se
Maria Roginskaya
Affiliation:
Chalmers University of Technology and the University of Gothenburg Email: p.ohrysko@gmail.commaria.roginskaya@chalmers.se
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Abstract

In this short note we first extend the validity of the spectral radius formula, obtained by M. Anoussis and G. Gatzouras, for Fourier–Stieltjes algebras. The second part is devoted to showing that, for the measure algebra on any locally compact non-discrete Abelian group, there are no non-trivial constraints among three quantities: the norm, the spectral radius, and the supremum of the Fourier–Stieltjes transform, even if we restrict our attention to measures with all convolution powers singular with respect to the Haar measure.

Keywords

measure algebraFourier–Stieltjes algebra

MSC classification

Primary: 43A10: Measure algebras on groups, semigroups, etc.
Secondary: 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 2 , June 2020 , pp. 269 - 275
Copyright
© Canadian Mathematical Society 2019

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Footnotes

Supported by foundations managed by The Royal Swedish Academy of Sciences.

References

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