Weak Compactness in the Dual Space of a Jb*-triple Is Commutatively Determined
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چکیده
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 (an) in the closed unit ball of E, a sequence (φn) in K , and θ > 0 satisfying that |φn(an)| > θ for all n ∈ N. This solves a question stimulated by the main result in [11] and posed in [9].
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تاریخ انتشار 2009