On operators acting on convergent sequences in Banach spaces

Our concern is to find a representation theorem for operators in B(c(X), c(Y)) where X and Y are Banach spaces with Y containing an isomorphic copy of co. Cass and GAO [1] obtained a representation theorem that always applies if Y does not contain an isomorphic copy of c(0). MADDOX [3], MELVIN-MELVIN [4], and ROBINSON [5] consider operators in B(c(X), c(Y)) that are given by matrices. In this paper we show that CASS'S and GAG'S result in [1] can be extended, when Y contains an isomorphic copy of c(0), to certain operators that we call representable. In addition, we show that when Y contains an isomorphic copy of c(0) there are always operators that fall outside the scope of our representation theorem. Light is also cast on a theorem given in MADDOX [3, Theorem 4.2] and [5, Theorem IV].