Abstract
AbstractWe study the complementation of the spaceW(X,Y) of weakly compact operators, the spaceK(X,Y) of compact operators, the spaceU(X,Y) of unconditionally converging operators, and the spaceCC(X,Y) of completely continuous operators in the spaceL(X,Y) of bounded linear operators fromXtoY. Feder proved that ifXis infinite-dimensional andc0↪Y, thenK(X,Y) is uncomplemented inL(X,Y). Emmanuele and John showed that ifc0↪K(X,Y), thenK(X,Y) is uncomplemented inL(X,Y). Bator and Lewis showed that ifXis not a Grothendieck space andc0↪Y, thenW(X,Y) is uncomplemented inL(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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
