Banach Journal of Mathematical Analysis

Homomorphisms of $l^1$-algebras on signed polynomial hypergroups

Rupert Lasser and Eva Perreiter

Full-text: Open access

Abstract

Let $\{R_n\}$ and $\{P_n\}$ be two polynomial systems which induce signed polynomial hypergroup structures on $\mathbb{N}_0.$ We investigate when the Banach algebra $l^1(\mathbb{N}_0,h^R)$ can be continuously embedded into or is isomorphic to $l^1(\mathbb{N}_0,h^P).$ We find sufficient conditions on the connection coefficients $ c_{nk} $ given by $ R_n = \sum_{k=0}^n c_{nk} P_k, $ for the existence of such an embedding or isomorphism. Finally we apply these results to obtain amenability-properties of the $l^1$-algebras induced by Bernstein-Szego and Jacobi polynomials.

Article information

Source
Banach J. Math. Anal., Volume 4, Number 2 (2010), 1-10.

Dates
First available in Project Euclid: 7 February 2011

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1297117237

Digital Object Identifier
doi:10.15352/bjma/1297117237

Mathematical Reviews number (MathSciNet)
MR2606478

Zentralblatt MATH identifier
1191.43005

Subjects
Primary: 43A62: Hypergroups
Secondary: 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

Citation

Lasser , Rupert; Perreiter , Eva. Homomorphisms of $l^1$-algebras on signed polynomial hypergroups. Banach J. Math. Anal. 4 (2010), no. 2, 1--10. doi:10.15352/bjma/1297117237. https://projecteuclid.org/euclid.bjma/1297117237


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