@article{1191.43005,
author="Lasser, Rupert and Perreiter, Eva",
title="{Homomorphisms of $l^1$-algebras on signed polynomial hypergroups.}",
language="English",
journal="Banach J. Math. Anal. ",
volume="4",
number="2",
pages="1-10",
year="2010",
abstract="{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.}",
reviewer="{Huoxiong Wu (Xiamen Fujian)}",
keywords="{Banach algebra homomorphism; hypergroup; amenability}",
classmath="{*43A62 (Hypergroups (abstract harmonic analysis))
43A22 (Homomorphisms and multipliers of function spaces on groups, etc.)
43A20 (L1 algebras on groups, etc.)
46H20 (Structure and classification of topological algebras)
}",
}