We study a property weaker than the Dunford–Pettis property, introduced by Freedman, in the case of a JB*-triple. It is shown that a JBW*-triple W has this property if, and only if, W is a Hilbert… (More)

These three questions had all been answered in the binary cases. Question 1 was answered affirmatively by Sakai [17] for C∗-algebras and by Upmeier [23] for JB -algebras. Question 2 was answered by… (More)

We prove that, ifE is a real JB*-triple having a predualE∗ , then E∗ is the unique predual of E and the triple product on E is separately σ(E,E∗)−continuous. Mathematics Subject Classification… (More)

A theorem of Lusin is proved in the non-ordered context of JB∗-triples. This is applied to obtain versions of a general transitivity theorem and to deduce refinements of facial structure in closed… (More)

A Banach space X is said to have the alternative Dunford-Pettis property if, whenever a sequence xn → x weakly in X with ‖xn‖ → ‖x‖, we have ρn(xn) → 0 for each weakly null sequence (ρn) in X∗. We… (More)

This paper relies on the important works of T. Barton and Y. Friedman [3] and C.-H. Chu, B. Iochum and G. Loupias [8] on the generalization of `Grothendieck's inequalities' to complex JB -triples. Of… (More)

We revise the concept of compact tripotent in the bidual space of a JB*-triple. This concept was introduced by Edwards and Rüttimann generalizing the ideas developed by Akemann for compact… (More)

It is shown that if P is a weak∗-continuous contractive projection on a JBW∗-triple M , then P(M) is of type I or semifinite, respectively, if M is of the corresponding type. We also show that P(M)… (More)

We prove that given a real JB*-triple E, and a real Hilbert space H , then the set of those bounded linear operators T from E toH , such that there exists a norm one functionalφ ∈ E∗ and… (More)

Let A be a type II von Neumann algebra with predual A∗. We prove that A∗ does not have the alternative Dunford–Pettis property introduced by W. Freedman [7], i.e., there is a sequence (φn) converging… (More)