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Hecke * -algebras on locally compact hypergroups

  • Seyyed Mohammad Tabatabaie EMAIL logo and Bentolhoda Sadathoseyni
Published/Copyright: November 7, 2020
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Abstract

In this paper, for a discrete hypergroup K and its subhypergroup H, we initiate the related Hecke * -algebra which is an extension of the classical one, and study its basic properties. Especially, we give a necessary and sufficient condition (named (β)) for this algebra to be associative. Also, we show that this new structure is an associative * -algebra if and only if K is a locally compact group.

MSC 2010: 43A62; 46L55; 43A20

Acknowledgements

Here, we thank professor Nigel Higson for his extremely useful advices on this work.

References

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Received: 2019-09-23
Revised: 2020-04-09
Accepted: 2020-04-24
Published Online: 2020-11-07
Published in Print: 2021-10-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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