Geodesic
Weak Sequential Completeness of K(X,Y)
Canadian mathematical bulletin, Tome 56 (2013) no. 3, pp. 503-509

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DOI

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.
DOI : 10.4153/CMB-2011-202-9
Mots-clés : 46B25, 46B28, weak sequential completeness, reflexivity, compact operator space 
Bu, Qingying. Weak Sequential Completeness of K(X,Y). Canadian mathematical bulletin, Tome 56 (2013) no. 3, pp. 503-509. doi: 10.4153/CMB-2011-202-9
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     title = {Weak {Sequential} {Completeness} of {K(X,Y)}},
     journal = {Canadian mathematical bulletin},
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     year = {2013},
     volume = {56},
     number = {3},
     doi = {10.4153/CMB-2011-202-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-202-9/}
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