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The Quarterly Journal of Mathematics 2004 55(4):441-450; doi:10.1093/qmath/hah017
© 2004 by Oxford University Press
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Multilinear extensions of Grothendieck's theorem

Fernando Bombal *, David Pérez-García § and Ignacio Villanueva ¶

Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, Madrid 28040, Spain  *  §

We introduce a new class of multilinear p-summing operators, which we call multiple p-summing. Using them, we can prove several multilinear generalizations of Grothendieck's ‘fundamental theorem of the metric theory of tensor products’. As an application we prove a vector-valued Littlewood's inequality.

Received 14 June 2002. Revised 5 February 2004.

* E-mail: bombal{at}mat.ucm.es

§ E-mail: David_Perez{at}mat.ucm.es

E-mail: ignaciov{at}mat.ucm.es


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