Abstract
In this paper, we study the concept of weakly almost periodic functions on Fréchet algebras. For a Fréchet algebra [Formula: see text], we show that [Formula: see text]. We also show that [Formula: see text] is Arens regular if and only if both [Formula: see text] and [Formula: see text] are Arens regular. Finally, for a sequence of Fréchet algebras [Formula: see text], we prove that the Fréchet algebra [Formula: see text] is Arens regualr if and only if each [Formula: see text] is Arens regular.
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