Let Dp (1 < p < < co , «here o = r (O co ) be the class of functions f, f(z) = S such that S i a„Vp |P a n , İ8 any fixed seguence of nonzero complex numbers satisfying lim < co). D under suitable topological and algebraîc structures foıms a P inf|v„i>'“ Banach algebra vvithout identify. The properties pertaining to quasi-invertible elements, topolo­ gical zero divisors ete. have been studied. Multiplîers and matrix transformations between Dp and various other known Frfechet spaces have been discussed.