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The linear space £ ( £ , F ) of all continuous linear maps of the Banach space E into a Banach space F is the completion olE'®F (all continuous linear maps with finite dimensional range) for a Hausdorff locally convex topology /. The topology / is the supremum of the strong operator topology [2, p. 475] and the topology of uniform convergence on the unit ball of E, F having the a(F,F') topology. The notation is patterned after [4]. In this context the result is stated in the following way.

The space of continuous linear operators as a completion of $E' \otimes F$