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. © 2024 the Author(s), licensee AIMS Press.