S. G Mikhlin (1908 – 1990)

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 c₀. Cass and Gao 1] obtained a representation theorem that always applies if Y does not contain an isomorphic copy of c₀. 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 Gao's result in 1] can be extended, when Y contains an isomorphic copy of c₀, to certain operators that we call represent able. In addition, we show that when Y contains an isomorphic copy of co 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].