Arens regularity of the Orlicz Figà-Talamanca Herz Algebra

2024/01/31 by Dabra, Arvish, Kumar, N. Shravan
#43A30 #46B22 #46J10 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 43A15 #Secondary 43A60

paper · doi:10.48550/arxiv.2401.17673

Abstract

Let G be a locally compact group and let A_Φ(G) be the Orlicz-version of the Figà-Talamanca Herz algebra of G associated with a Young function Φ. We show that if A_Φ(G) is Arens regular, then G is discrete. We further explore the Arens regularity of A_Φ(G) when the underlying group G is discrete. In the running, we also show that A_Φ(G) is finite-dimensional if and only if G is finite. Further, for amenable groups, we show that A_Φ(G) is reflexive if and only if G is finite, under the assumption that the associated Young function Φ satisfies the MA-condition.

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