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1. CMB 2011 (vol 55 pp. 449)

Bahreini, Manijeh; Bator, Elizabeth; Ghenciu, Ioana
 Complemented Subspaces of Linear Bounded Operators We study the complementation of the space \$W(X,Y)\$ of weakly compact operators, the space \$K(X,Y)\$ of compact operators, the space \$U(X,Y)\$ of unconditionally converging operators, and the space \$CC(X,Y)\$ of completely continuous operators in the space \$L(X,Y)\$ of bounded linear operators from \$X\$ to \$Y\$. Feder proved that if \$X\$ is infinite-dimensional and \$c_0 \hookrightarrow Y\$, then \$K(X,Y)\$ is uncomplemented in \$L(X,Y)\$. Emmanuele and John showed that if \$c_0 \hookrightarrow K(X,Y)\$, then \$K(X,Y)\$ is uncomplemented in \$L(X,Y)\$. Bator and Lewis showed that if \$X\$ is not a Grothendieck space and \$c_0 \hookrightarrow Y\$, then \$W(X,Y)\$ is uncomplemented in \$L(X,Y)\$. In this paper, classical results of Kalton and separably determined operator ideals with property \$(*)\$ are used to obtain complementation results that yield these theorems as corollaries. Keywords:spaces of operators, complemented subspaces, compact operators, weakly compact operators, completely continuous operatorsCategories:46B20, 46B28

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