# Generalized multiple summing multilinear operators on Banach spaces

## TL;DR

This paper introduces a unified abstract framework for multiple summing multilinear operators on Banach spaces, encompassing known classes and defining new subclasses with shared properties.

## Contribution

It provides a unifying approach to various classes of multiple summing operators and introduces new subclasses within this framework.

## Key findings

- Unified treatment of multiple summing operator classes
- Extension of known classes to a broader abstract setting
- Introduction of new subclasses with inherited properties

## Abstract

In this paper we provide an abstract aproach to the study of classes of multiple summing multilinear operators between Banach spaces. The main purpose is unify the study of several known classes and results, for example multiple $(p, q_1,\dots, q_n)$-summing operators, multiple mixing $(s, q, p)$-summing operators and multiple strong $(s, q, p)$-mixing summing operators. We also define new class of multiple summing multilinear operator that are particular cases of our construction and, therefore, satisfy the results proved in the paper.