Abstract
Suppose X and Y are FK spaces in which ϕ the span of the coordinate vectors (en) is dense. Let L(X,Y) denote the space of all matrices of the form Ei(T(ej)) as T ranges over all continuous linear operators from X into Y; here ei represents the ith coordinate vector and Ei represents the ith coordinate functional. Let M(L(X, Y)) denote the space of all matrices B such that (B(i,j)A(i,j)) is in L(X,Y) whenever A is in L(X,Y). In this paper we shall show how the summability properties of X and Y determine the extent of M(L(X,Y)) and conversely how the extent of M(L(X,Y)) determines the summability properties of both X and Y.
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