Remarks on weak amenability of hypergroups

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.