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arXiv · 1311.4685

Weak compactness and strongly summing multilinear operators

Daniel Pellegrino·Pilar Rueda·Enrique A. Sanchez-Perez
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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.

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Daniel Pellegrino, Pilar Rueda, Enrique A. Sanchez-Perez. 2013-11-19. Weak compactness and strongly summing multilinear operators. https://arxiv.org/abs/1311.4685

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