This is an announcement for the paper "Weak compactness and strongly summing multilinear operators" by Daniel Pellegrino, Pilar Rueda, and Enrique A. Sanchez-Perez.

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.

Archive classification: math.FA

Mathematics Subject Classification: 46A32

Submitted from: pilar.rueda@uv.es

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

http://front.math.ucdavis.edu/1311.4685

or

http://arXiv.org/abs/1311.4685