A standard technique in infinite dimensional holomorphy, which produced several useful results, uses the Borel transform to represent linear functionals on certain spaces of multilinear operators between Banach spaces as multilinear operators. In this paper we develop a technique to represent linear functionals, as linear operators, on spaces of multilinear operators that are beyond the scope of the standard technique. Concrete applications to some well studied classes of multilinear operators, including the class of compact multilinear operators, and to one new class are provided. We can see, in particular, that sometimes our representations hold under conditions less restrictive than those of the related classical ones.

中文翻译：

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关于多重线性算子超理想上线性泛函的表示

产生若干有用结果的无限维全纯中的一种标准技术使用 Borel 变换将 Banach 空间之间的多线性算子的某些空间上的线性泛函表示为多线性算子。在本文中，我们开发了一种技术，可以在超出标准技术范围的多线性运算符空间上将线性泛函表示为线性运算符。提供了对一些经过充分研究的多线性算子类（包括紧凑型多线性算子类）和一个新类的具体应用。我们可以看到，特别是，有时我们的表示在比相关经典表示的限制更少的条件下成立。