Annals of Functional Analysis

Some consequences of spectral synthesis in hypergroup algebras

B. E. Forrest

Abstract

Properties of spectral synthesis are exploited to show that, for a large class of commutative hypergroups and for every compact hypergroup, every closed, reflexive, left-translation-invariant subspace of $L^{\infty}(K)$ is finite-dimensional. Also, we show that, for a class of hypergroups which includes many commutative hypergroups and all $\mathcal{Z}$-hypergroups, every derivation of $L^{1}(K)$ into an arbitrary Banach $L^{1}$-bimodule is continuous.

Article information

Source
Ann. Funct. Anal., Volume 7, Number 1 (2016), 170-179.

Dates
Accepted: 11 August 2015
First available in Project Euclid: 22 December 2015

https://projecteuclid.org/euclid.afa/1450803724

Digital Object Identifier
doi:10.1215/20088752-3428456

Mathematical Reviews number (MathSciNet)
MR3449349

Zentralblatt MATH identifier
06553494

Subjects
Primary: 43A62: Hypergroups
Secondary: 46H40: Automatic continuity

Citation

Forrest, B. E. Some consequences of spectral synthesis in hypergroup algebras. Ann. Funct. Anal. 7 (2016), no. 1, 170--179. doi:10.1215/20088752-3428456. https://projecteuclid.org/euclid.afa/1450803724

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