Annals of Functional Analysis

Some consequences of spectral synthesis in hypergroup algebras

B. E. Forrest

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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(K) is finite-dimensional. Also, we show that, for a class of hypergroups which includes many commutative hypergroups and all Z-hypergroups, every derivation of L1(K) into an arbitrary Banach L1-bimodule is continuous.

Article information

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

Dates
Received: 15 March 2015
Accepted: 11 August 2015
First available in Project Euclid: 22 December 2015

Permanent link to this document
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

Keywords
hypergroup algebras spectral synthesis Fourier algebra

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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