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

TL;DR

This paper introduces a new technique to represent linear functionals on spaces of multilinear operators, extending beyond traditional methods and applying to classes like compact operators with less restrictive conditions.

Contribution

Develops a novel approach to represent linear functionals on multilinear operator spaces, surpassing the limitations of the standard Borel transform technique.

Findings

New representation technique for multilinear operators

Applicable to classes like compact multilinear operators

Conditions for representation can be less restrictive

Abstract

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.