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arXiv · 2201.01258

On the Arens regularity of Frechet algebras and their biduals

Zahra Alimohammadi·Ali Rejali
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Abstract

In This paper, we study the concept of weakly almost periodic functions on Frechet algebras. For a Frechet algebra A, we show that WAP(A)=wap(A). We also show that A** is Arens regular if and only if both A and WAP(A)* are Arens regular. Finally, for a sequence of Frechet algebras (An), we prove that the Frechet algebra \ell^1-\prod An is Arens regular if and only if each An is Arens regular.

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Zahra Alimohammadi, Ali Rejali. 2022-01-04. On the Arens regularity of Frechet algebras and their biduals. https://arxiv.org/abs/2201.01258

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