On nonlinear absolutely summing maps

TL;DR

This paper proves that the nonlinear Pietsch Domination Theorem holds without the need for the (sub)-homogeneity assumption, strengthening the theorem and exploring its implications.

Contribution

It demonstrates that the nonlinear Pietsch Domination Theorem remains valid without the (sub)-homogeneity hypothesis, providing a stronger version of the theorem.

Findings

The theorem is valid without (sub)-homogeneity assumptions.

The stronger version of the nonlinear Pietsch Domination Theorem is established.

Several consequences of this strengthened theorem are discussed.

Abstract

It is shown that the ultimate version of the nonlinear Pietsch Domination Theorem remains true, even in a stronger presentation, if one of its hypotheses is removed. More precisely, we show that no trace of (sub)-homogeneity assumption is needed. Some consequences are also presented.