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

Canadian mathematical bulletin

Qingying Bu¹ 

[1] Department of Mathematics, University of Mississippi, University, MS 38677, USA

关键词: weak sequential completeness;    reflexivity;    compact operator space;   

DOI  :  10.4153/CMB-2011-202-9

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

For Banach spaces $X$ and $Y$, we show that if $X^ast$ and $Y$ areweakly 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 compactapproximation property.

【 授权许可】

Unknown