  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.
