Weak compactness and strongly summing multilinear operators
Functional Analysis
2013-11-20 v1
Abstract
Every absolutely summing linear operator is weakly compact. However, for strongly summing multilinear operators and polynomials - one of the most natural extensions of the linear case to the non linear framework - weak compactness does not hold in general. We show that a subclass of the class of strongly summing multilinear operators/polynomials, sharing its main properties such as Grothendieck's Theorem, Pietsch Domination Theorem and Dvoretzky-Rogers Theorem, has even better properties like weak compactness and a natural factorization theorem.
Cite
@article{arxiv.1311.4685,
title = {Weak compactness and strongly summing multilinear operators},
author = {Daniel Pellegrino and Pilar Rueda and Enrique A. Sanchez-Perez},
journal= {arXiv preprint arXiv:1311.4685},
year = {2013}
}