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Proceedings of the American Mathematical Society

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Sliding hump technique and spaces with the Wilansky property


Authors: Dominikus Noll and Wolfgang Stadler
Journal: Proc. Amer. Math. Soc. 105 (1989), 903-910
MSC: Primary 46A45; Secondary 40D25, 46A07
DOI: https://doi.org/10.1090/S0002-9939-1989-0989099-7
MathSciNet review: 989099
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Abstract: We prove that if $ E$ is a BK- AK-space whose dual $ E'$ as well is BK- AK , then $ \sigma (E',F)$ and $ \sigma (E',F)$ have the same convergent sequences whenever $ F$ is a subspace of $ E''$ containing $ \Phi $ and satisfying $ {F^\beta } = {E^\beta }$. This extends a result due to Bennett [B$ _{2}$] and the second author [S]. We provide new examples of BK-spaces having the Wilansky property. We show that the bidual $ E''$ of a solid BK- AK-space $ E$ whose dual as well is BK- AK satisfies a separable version of the Wilansky property. This extends a theorem of Bennett and Kalton, who proved that $ {l^\infty }$ has the separable Wilansky property.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0989099-7
Keywords: Sliding hump technique, BK-spaces, spaces with the Wilansky property
Article copyright: © Copyright 1989 American Mathematical Society