Sliding hump technique and spaces with the Wilansky property

Noll, Dominikus; Stadler, Wolfgang

doi:10.1090/S0002-9939-1989-0989099-7

Sliding hump technique and spaces with the Wilansky property
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by Dominikus Noll and Wolfgang Stadler PDF

Proc. Amer. Math. Soc. 105 (1989), 903-910 Request permission

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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