Spectra of L(1)-convolution operators acting on L(p)-spaces of commutative hypergroups

Author:

Perreiter, Eva  

Journal:

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY

Issue Date:

2011

Abstract(summary):

We show that, for commutative hypergroups, the spectrum of all L(1)-convolution operators on L(p) is independent of p is an element of [1, infinity] exactly when the Plancherel measure is supported on the whole character space chi(b)(K), i.e., exactly when L(1)(K) is symmetric and for every alpha is an element of (K)over cap Reiter's condition P(2) holds true. Furthermore, we explicitly determine the spectra sigma(p)(T(epsilon 1)) for the family of Karlin-McGregor polynomial hypergroups, which demonstrate that in general the spectra might even be different for each p.

Page:

503---519