Weak compactness in the dual space of a JB*-triple is commutatively determined

• Autores: Francisco José Fernández Polo , Antonio Miguel Peralta Pereira
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 105, Nº 2, 2009, págs. 307-319
• Idioma: inglés
• DOI: 10.7146/math.scand.a-15120
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• Resumen

  • 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].