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Weak Sequential Completeness of $\mathcal K(X,Y)$

  Published:2012-03-05
 Printed: Sep 2013
  • Qingying Bu,
    Department of Mathematics, University of Mississippi, University, MS 38677, USA
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Abstract

For Banach spaces $X$ and $Y$, we show that if $X^\ast$ 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 $X^\ast$ or $Y$ has the bounded compact approximation property.
Keywords: weak sequential completeness, reflexivity, compact operator space weak sequential completeness, reflexivity, compact operator space
MSC Classifications: 46B25, 46B28 show english descriptions Classical Banach spaces in the general theory
Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]
46B25 - Classical Banach spaces in the general theory
46B28 - Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]
 

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