Coincidence results for summing multilinear mappings

TL;DR

This paper establishes new coincidence results for spaces of absolutely summing multilinear mappings between Banach spaces, introducing techniques to extend known linear and multilinear results to more general cases.

Contribution

It provides optimal generalizations of existing results and introduces novel methods to extend coincidence results across various multilinear mappings.

Findings

Proved coincidence results for summing multilinear mappings.

Developed techniques to extend linear and multilinear results.

Enhanced understanding of summability in Banach space mappings.

Abstract

In this paper we prove coincidence results concerning spaces of absolutely summing multilinear mappings between Banach spaces. The nature of these results arises from two distinct approaches: the coincidence of two \textit{a priori} different classes of summing multilinear mappings and the summability of all multilinear mappings defined on products of Banach spaces. Optimal generalizations of known results are obtained. We also introduce and explore new techniques in the field, for example a technique to extend coincidence results for linear, bilinear and even trilinear mappings to general multilinear ones.