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

Authors

  • Francisco J. Fernández-Polo
  • Antonio M. Peralta

DOI:

https://doi.org/10.7146/math.scand.a-15120

Abstract

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 nN. This solves a question stimulated by the main result in [11] and posed in [9].

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Published

2009-12-01

How to Cite

Fernández-Polo, F. J., & Peralta, A. M. (2009). Weak compactness in the dual space of a JB*-triple is commutatively determined. MATHEMATICA SCANDINAVICA, 105(2), 307–319. https://doi.org/10.7146/math.scand.a-15120

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Articles