Remarks on weak amenability of hypergroups

Authors

  • Mahmood Alaghmandan Ottawa, ON, Canada

DOI:

https://doi.org/10.3842/umzh.v77i5.7943

Keywords:

weak amenability, Fourier algebra, completely bounded multipliers, Leptin theorem, ultraspherical hypergroups

Abstract

UDC 512.5

We study the existence of multiplier (completely) bounded  approximate identities for the Fourier algebras of some classes of  hypergroups. In particular, it is shown that, the hypergroups from a large class of commutative hypergroups are weakly amenable with the Cowling–Haagerup constant $1$.  As a corollary, we  answer an open question of Eymard about Jacobi hypergroups. We also characterize the existence of  bounded approximate identities for the hypergroup Fourier algebras of spherical hypergroups.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 77, No. 5, 2025.

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Published

04.07.2025

Issue

Vol. 77 No. 5 (2025)

Section

Research articles

License

Copyright (c) 2025 Mahmood Alaghmandan

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Alaghmandan, Mahmood. “Remarks on Weak Amenability of Hypergroups”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 5, July 2025, pp. 364–365, https://doi.org/10.3842/umzh.v77i5.7943.