an: Zbl 1191.43005
au: Lasser, Rupert; Perreiter, Eva
ti: Homomorphisms of $l^1$-algebras on signed polynomial hypergroups.
la: EN
so: Banach J. Math. Anal. 4, No. 2, 1-10, electronic only (2010).
py: 2010
dt: J
cc: *43A62 43A22 43A20 46H20
ut: Banach algebra homomorphism; hypergroup; amenability
ab: Let $\{R_n\}$ and $\{P_n\}$ be two polynomial systems which induce signed
    polynomial hypergroup structures on $N_0$. The paper under review
    investigates when the Banach algebra $l^1(N_0, h^R)$ can be continuously
    embedded into or is isomorphic to $l^1(N_0, h^P)$. Certain sufficient
    conditions on the connection coefficients $c_{n,k}$ given by
    $R_n=\sum_{k=0}^n c_{nk}P_k$, for the existence of such an embedding or
    isomorphism are given. These results are also applied to obtain amenability
    properties of the $l^1$-algebras induced by Bernstein-Szeg\H o and Jacobi
    polynomials.
 
 The previous related investigations can be found in {\it W.
    R. Bloom} and {\it M. E. Walter}'s work [J. Aust. Math. Soc., Ser. A 52, No.
    3, 383--400 (1992; Zbl 0776.43001)], which was only concerned with the
    isometric isomorphisms of hypergroups. For more recent works, see {\it R.
    Lasser}'s articles [Stud. Math. 182, No. 2, 183--196 (2007; Zbl 1126.43003);
    Colloq. Math. 116, No. 1, 15--30 (2009; Zbl 1167.43007)], which studied the
    amenability of $l^1$-algebras of polynomial hypergroups.
rv: Huoxiong Wu (Xiamen Fujian)
ci: Zbl 0776.43001; Zbl 1126.43003; Zbl 1167.43007