Grothendieck's Inequalities for Real and Complex JBW*-Triples |
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Authors: | Peralta Antonio M; Palacios Angel Rodriguez |
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Institution: | Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada 18071 Granada, Spain, aperalta{at}goliat.ugr.es, apalacio{at}goliat.ugr.es |
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Abstract: | We prove that, if and >0, if V and W are complex JBW*-triples (with preduals V* andW*, respectively), and if U is a separately weak*-continuousbilinear form on V x W, then there exist norm-one functionals1, 2 V* and 1, 2 W* satisfying
for all (x, y) V x W. Here, for a norm-one functional on acomplex JB*-triple V, |·| stands for the prehilbertianseminorm on V associated to given by for all x W, where z V** satisfies z = |z| =1. We arrive at this form of Grothendieck's inequalitythrough results of C.-H. Chu, B. Iochum, and G. Loupias, andan amended version of the little Grothendieck's inequalityfor complex JB*-triples due to T. Barton and Y. Friedman. Wealso obtain extensions of these results to the setting of realJB*-triples. 2000 Mathematical Subject Classification: 17C65,46K70, 46L05, 46L10, 46L70. |
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Keywords: | Grothendieck's inequalities real and complex JB* and JBW*-triples strong*-topology |
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