## Annals of Functional Analysis

### Approximate amenability and contractibility of hypergroup algebras

#### 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 $L_{\infty}(K,L(K))$ and prove that the dual of a Banach hypergroup algebra $L(K)$ can be identified with $L_{\infty}(K,L(K))$. 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

#### 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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