Lasser, Rupert; Perreiter, Eva Homomorphisms of \(l^1\)-algebras on signed polynomial hypergroups. (English) Zbl 1191.43005 Banach J. Math. Anal. 4, No. 2, 1-10 (2010). 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-Szegő and Jacobi polynomials.The previous related investigations can be found in W. R. Bloom and 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 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) Cited in 5 Documents MSC: 43A62 Harmonic analysis on hypergroups 43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 43A20 \(L^1\)-algebras on groups, semigroups, etc. 46H20 Structure, classification of topological algebras Keywords:Banach algebra homomorphism; hypergroup; amenability Citations:Zbl 0776.43001; Zbl 1126.43003; Zbl 1167.43007 PDFBibTeX XMLCite \textit{R. Lasser} and \textit{E. Perreiter}, Banach J. Math. Anal. 4, No. 2, 1--10 (2010; Zbl 1191.43005) Full Text: DOI EuDML EMIS