The Dunford-Pettis and the Kadec-Klee properties on tensor products of JB*-triples

We prove that for every member X in the class of real or complex JB * -triples or preduals of JBW * -triples, the following assertions are equivalent:(1) X has the fixed point property.(2) X has the super fixed point property.(3) X has normal structure.(4) X has uniform normal structure. (5) The Banach space of X is reflexive.As a consequence, a real or complex C * -algebra or the predual of a real or complex W * -algebra having the fixed point property must be finite-dimensional.

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The Dunford-Pettis and the Kadec-Klee properties on tensor products of JB*-triples

Cited by 6 publications

References 27 publications

The alternative Dunford-Pettis property on projective tensor products

The alternative Dunford-Pettis property on projective tensor products

Dunford–Pettis properties, Hilbert spaces and projective tensor products

The fixed point property inJB∗-triples and preduals ofJBW∗-triples

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