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
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