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arXiv · 2401.17673

Arens regularity of the Orlicz Fig\`a-Talamanca Herz Algebra

Arvish Dabra·N. Shravan Kumar
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Abstract

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

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Arvish Dabra, N. Shravan Kumar. 2024-01-31. Arens regularity of the Orlicz Fig\`a-Talamanca Herz Algebra. https://arxiv.org/abs/2401.17673

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