This is an announcement for the paper "Lineability and uniformly dominated sets of summing nonlinear" by Daniel Pellegrino and Joedson Santos.

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.

Archive classification: math.FA

Submitted from: pellegrino@pq.cnpq.br

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1411.1100

or

http://arXiv.org/abs/1411.1100