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Spectra of L1-convolution operators acting on Lp-spaces of commutative hypergroups

Published online by Cambridge University Press:  18 July 2011

EVA PERREITER
EVA PERREITER*
Affiliation:
Institute of Biomathematics and Biometry, Helmholtz Zentrum München, 85764 Neuherberg, Germany. e-mail: eva.perreiter@helmholtz-muenchen.de
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Abstract

We show that, for commutative hypergroups, the spectrum of all L1-convolution operators on Lp is independent of p ∈ [1, ∞] exactly when the Plancherel measure is supported on the whole character space χb(K), i.e., exactly when L1(K) is symmetric and for every α ∈ Reiter's condition P2 holds true. Furthermore, we explicitly determine the spectra σp(Tϵ1) for the family of Karlin–McGregor polynomial hypergroups, which demonstrate that in general the spectra might even be different for each p.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 151 , Issue 3 , November 2011 , pp. 503 - 519
Copyright
Copyright © Cambridge Philosophical Society 2011

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References

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