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The Spectral Radius Formula for Fourier–Stieltjes Algebras

Published online by Cambridge University Press:  22 July 2019

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

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.

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Article
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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