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Weak Sequential Completeness of 𝑲(X,Y)
Published online by Cambridge University Press: 20 November 2018
Abstract
For Banach spaces $X$ and
$Y$, we show that if
${{X}^{*}}$ and
$Y$ are weakly sequentially complete and every weakly compact operator from
$X$ to
$Y$ is compact, then the space of all compact operators from
$X$ to
$Y$ is weakly sequentially complete. The converse is also true if, in addition, either
${{X}^{*}}$ or
$Y$ has the bounded compact approximation property.
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- Research Article
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- Copyright © Canadian Mathematical Society 2013
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