Multiple almost summing operators

TL;DR

This paper introduces the concept of multiple almost summing multilinear operators, defining new types and cotypes, and demonstrates their properties as Banach multi-ideals with coherence and compatibility features.

Contribution

It presents a novel framework for multiple almost summing operators, extending the theory of multilinear operator types and cotypes with new Banach multi-ideals.

Findings

The classes of multiple almost summing operators are Banach multi-ideals.

The new concepts recover classical type and cotype for multilinear operators.

The classes are coherent and compatible with generated homogeneous polynomials.

Abstract

In this paper, we explore the concept of multilinear operators that are multiple almost summing and present a new concept of type and cotype of multilinear operators and investigate the conditions for this new concept to recover the original concept of type and type for multilinear operators. We also show that these classes are Banach multi-ideals and establish the coherence and compatibility of these classes with the generated homogeneous polynomials.