Canadian Mathematical Bulletin (14964287)55(3)pp. 449-461
We study the complementation of the spaceW(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 → Y, then K(X,Y) is uncomplemented in L(X,Y). Emmanuele and John showed that if c 0 → 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 → 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. © Canadian Mathematical Society 2011.
