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].
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