Summing multilinear operators and sequence classes

TL;DR

This paper develops a comprehensive framework for classes of multilinear operators between Banach spaces, unifying various summing operator classes and establishing their Banach ideal properties with applications to coherence and coincidence theorems.

Contribution

It introduces a general construction that encompasses multiple existing classes of summing multilinear operators, providing a unified approach and new theoretical insights.

Findings

The classes form Banach ideals of multilinear operators.

The framework includes summing operators by blocks in isotropic and anisotropic cases.

Applications to coherence and coincidence theorems are demonstrated.

Abstract

We construct a general framework that generates classes of multilinear operators between Banach spaces which encompasses, as particular cases, the several classes of summing type multilinear operators that have been studied individually in the literature. Summing operators by blocks in the isotropic and anisotropic cases are taken into account. The classes we create are shown to be Banach ideals of multilinear operators and applications to coherence and coincidence theorems are provided.