1. Let E denote a Banacb space över the fieîd of real or conıplex numbers. The spaces Co(E), c(E), t.p(E) and loo(E) of sequences in E have been discussed by Boas [1], Day [2], Leonard [9], Maddox [11] and some others. Lorentz [10] introduced the space c cf aîmost convergent sequen- ces of real or complex numbers. Subsequently almost cf nvergent scqu- ences have been discussed by Duran [5], Kiug [6], Nanda [14, 15] and some others. The space c (E) of almost convergent sequenees in E has been discussed by Kurtz [7, 8]. More recently some new sequence spaces. ■vvhich. are denoted by tp and î P> space 'ip of sequences of real or absolute analogue, just as have been introduced in [3] and [4], The complex numbers emerged from c as iîs ip emerged from tîıe concept of convergence.