Annals of Functional Analysis

Approximate amenability and contractibility of hypergroup algebras

J. Laali and R. Ramezani

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Abstract

Let K be a hypergroup. The purpose of this article is to study the notions of amenability of the hypergroup algebras L(K), M(K), and L(K). Among other results, we obtain a characterization of approximate amenability of L(K). Moreover, we introduce the Banach space L(K,L(K)) and prove that the dual of a Banach hypergroup algebra L(K) can be identified with L(K,L(K)). In particular, L(K) is an F-algebra. By using this fact, we give necessary and sufficient conditions for K to be left-amenable.

Article information

Source
Ann. Funct. Anal., Volume 9, Number 4 (2018), 551-565.

Dates
Received: 16 October 2017
Accepted: 7 January 2018
First available in Project Euclid: 10 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.afa/1539137305

Digital Object Identifier
doi:10.1215/20088752-2018-0001

Mathematical Reviews number (MathSciNet)
MR3871914

Zentralblatt MATH identifier
07002091

Subjects
Primary: 43A62: Hypergroups
Secondary: 46K05: General theory of topological algebras with involution 43A07: Means on groups, semigroups, etc.; amenable groups

Keywords
hypergroup approximate amenability involution left-amenable

Citation

Laali, J.; Ramezani, R. Approximate amenability and contractibility of hypergroup algebras. Ann. Funct. Anal. 9 (2018), no. 4, 551--565. doi:10.1215/20088752-2018-0001. https://projecteuclid.org/euclid.afa/1539137305


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