The dual of a space of compact operators - Keun Young Lee; Gwanghyun Jo (AIMS Mathematics, 2024)
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 $ \mathcal{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.