The dual of a space of compact operators

Abstract

Let X and Y be Banach spaces. We provide the representation of the dual space of compact operators K(X,Y) as a subspace of bounded linear operators L(X,Y). The main results are: (1) If Y is separable, then the dual forms of K(X,Y) can be represented by the integral operator and the elements of C[0,1]. (2) If X** has the weak Radon-Nikodym property, then the dual forms of K(X,Y) can be represented by the trace of some tensor products.