Lineability and uniformly dominated sets of summing nonlinear operators

Abstract: In this note we prove an abstract version of a result from 2002 due to Delgado and Pi~{n}ero on absolutely summing operators. Several applications are presented; some of them in the multilinear framework and some in a completely nonlinear setting. In a final section we investigate the size of the set of non uniformly dominated sets of linear operators under the point of view of lineability.