About an isomorphism between the Beurling algebra with a weight dependent convolution and the L¹(G) group algebra

2025/03/18 by Rodríguez-Barrera, Raúl, Torres-Ayala, Francisco
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2503.14249

Abstract

We show that the Beurling algebra with a weight-dependent convolution and the group algebra L¹(G) are isomorphic. In particular, using this isomorphism, we extend some results of the algebra \mathscrL¹(G,ω) presented in recent articles. As a main result, we explicitly construct the equivalence between unitary representations of the group and non-degenerate ∗-representations of this algebra.

Related

• Non-weakly amenable Beurling algebras
• Some weighted group algebras are operator algebras
• An Algebra Containing the Two-Sided Convolution Operators
• Weak amenability of weighted group algebras
• Some Beurling-Fourier algebras on compact groups are operator algebras