On summability of nonlinear mappings: a new approach

TL;DR

This paper introduces a new approach to characterize nonlinear mappings between Banach spaces that satisfy a Pietsch Domination-type theorem, leading to a natural notion of weighted summability.

Contribution

It provides a novel characterization of nonlinear mappings satisfying a domination theorem and introduces the concept of weighted summability.

Findings

Characterization of nonlinear mappings satisfying Pietsch-type domination.

Introduction of a natural weighted summability concept.

Potential for further research into weighted summability.

Abstract

The main goal of this paper is to characterize arbitrary nonlinear (non-multilinear) mappings $f:X_{1}\times...\times X_{n}\rightarrow Y$ between Banach spaces that satisfy a quite natural Pietsch Domination-type theorem around a given point $(a_{1},...,a_{n})\in$ $X_{1}\times...\times X_{n}$. As a consequence of our approach a notion of weighted summability arises naturally, which may be an interesting topic for further investigation.