Articles
Iranian Journal of Science and Technology, Transaction A: Science (10286276)42(4)pp. 2289-2292
In this paper, we study how some localized properties, e.g., Dunford–Pettis sets, and V*-sets can be used to study more global structure properties. We introduce a new class of Banach spaces called Banach spaces with property (MB*). We say that a space X has property (MB*) if every V*-set in X is a Dunford–Pettis set in X. We characterize those spaces which have property (MB*). It is shown that X has property (MB*) if and only if for every Banach space Y, every unconditionally converging adjoint operator T* from X* to Y* is completely continuous. Also, we recall property (MB) for Banach spaces and then study relation between these two properties. © 2018, Shiraz University.
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.
