Complemented Subspaces of Linear Bounded Operators

Canadian mathematical bulletin

Ioana Ghenciu¹  Elizabeth Bator³  Manijeh Bahreini² 

[1] University of Wisconsin-River Falls, Department of Mathematics, River Falls, WI 54022-5001;University of Isfahan, Department of Mathematics, Isfahan 81745-163, Iran;University of North Texas, Department of Mathematics, Denton, Texas 76203-1430

关键词: spaces of operators;    complemented subspaces;    compact operators;    weakly compact operators;    completely continuous operators;   

DOI  :  10.4153/CMB-2011-097-2

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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 $c_0hookrightarrow Y$, then $K(X,Y)$ is uncomplemented in$L(X,Y)$. Emmanuele and John showed that if $c_0 hookrightarrowK(X,Y)$, 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 separablydetermined operator ideals with property $(*)$ are used to obtaincomplementation results that yield these theorems as corollaries.

【 授权许可】

Unknown