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A standard technique in infinite dimensional holomorphy, which producedseveral useful results, uses the Borel transform to represent linearfunctionals on certain spaces of multilinear operators between Banach spaces asmultilinear operators. In this paper we develop a technique to represent linearfunctionals, as linear operators, on spaces of multilinear operators that arebeyond the scope of the standard technique. Concrete applications to some wellstudied classes of multilinear operators, including the class of compactmultilinear operators, and to one new class are provided. We can see, inparticular, that sometimes our representations hold under conditions lessrestrictive than those of the related classical ones.

On the representation of linear functionals on hyper-ideals of multilinear operators