Best approximation in spaces of compact operators

Let K(X,Y) be the space of compact operators. For a proximinal subspace Z⊂Y, this paper deals with question, when does every Y-valued operator admit Z-valued best approximation? any reflexive Banach X and for L1-predual Y, if Z⊂Y is strongly finite codimension, we show that K(X,Z) under an additional condition on position K(X,Z). When Y c0-direct sum dimensional spaces achieve strong transitivity result by showing codimension bounded admits approximation.