Abstract
Throughout, X and Y will be nontrivial normed linear spaces over the field of complex numbers, E the space ?(X, Y) of continuous linear transformations from X into Y equipped with the usual norm, which we denote by ,u, W a linear subspace of the dual Y' of Y, and co the set of positive integers. The norm-closed unit ball in X, for example, is written Sx, and the canonical embedding q5 from Y into W' is defined by +k(y) (w) = w(y). Each f belonging to the tensor product X 0 W determines a continuous linear functional on E since if EJx, Xi wi is any representation of f then
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