Weak compactness in the dual space of a JB*-triple is commutatively determined - Fernández-Polo, Francisco J.; Peralta, Antonio M. (MATHEMATICA SCANDINAVICA, 2009)
We prove the following criterium of weak compactness in the dual of a JB*-triple: a bounded set K in the dual of a JB*-triple E is not relatively weakly compact if and only if there exist a sequence of pairwise orthogonal elements (a_n) in the closed unit ball of E, a sequence (φ_n ) in K, and ϑ >0 satisfying that |φ_n(a_n)|>ϑ for all n N. This solves a question stimulated by the main result in [11] and posed in [9].