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November 2017 Involutions in algebras related to second duals of hypergroup algebras
Alireza Medghalchi, Ramin Ramezani
Ann. Funct. Anal. 8(4): 547-556 (November 2017). DOI: 10.1215/20088752-2017-0036

Abstract

Let K be a hypergroup. The purpose of this article is to study the question of involutions on algebras M(K), L(K), and Lc(K). We show that the natural involution of M(K) has the canonical extension to M(K) if and only if the natural involution of L(K) has the canonical extension to L(K). Also, we give necessary and sufficient conditions for M(K) and L(K) to admit an involution extending the natural involution of M(K) when K is left amenable. Finally, we find the necessary and sufficient conditions for Lc(K) to admit an involution.

Citation

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Alireza Medghalchi. Ramin Ramezani. "Involutions in algebras related to second duals of hypergroup algebras." Ann. Funct. Anal. 8 (4) 547 - 556, November 2017. https://doi.org/10.1215/20088752-2017-0036

Information

Received: 7 December 2016; Accepted: 17 April 2017; Published: November 2017
First available in Project Euclid: 8 September 2017

zbMATH: 1382.43011
MathSciNet: MR3717176
Digital Object Identifier: 10.1215/20088752-2017-0036

Subjects:
Primary: 43A62
Secondary: ‎43A07‎, 46K05

Rights: Copyright © 2017 Tusi Mathematical Research Group

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Vol.8 • No. 4 • November 2017
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