Cohen factorable p-nuclear multilinear operators

TL;DR

This paper extends the theory of p-nuclear operators to multilinear and polynomial contexts, establishing new ideals and key theorems like Pietsch domination and Cohen-Kwapien factorization.

Contribution

It introduces multilinear and polynomial ideals for p-nuclear operators, adapting core theorems from linear operator theory to these new classes.

Findings

Established Pietsch domination theorem for p-nuclear multilinear operators.

Developed Cohen-Kwapien type factorization for p-nuclear polynomials.

Extended the framework of p-nuclear operators to multilinear and polynomial settings.

Abstract

Basing on the work of Pellegrino et al. on factorable strongly p-summing multilinear operators, we will continue study this class of operators and borrowing the same idea for the category of p-nuclear operators. Therefore, we will construct other multilinear and polynomial ideals for which the most valuable results of the theory of p-nuclear linear operators are available, namely the Pietsch domination theorem and the well known factorization given by Cohen and Kwapien for p-nuclear operators.