Dual spaces of compact operator spaces and the weak Radon–Nikodým property
Volume 210 / 2012
Studia Mathematica 210 (2012), 247-260
MSC: Primary 46B22; Secondary 46B28.
DOI: 10.4064/sm210-3-5
Abstract
We deal with the weak Radon–Nikodým property in connection with the dual space of $\mathcal{K}(X,Y)$, the space of compact operators from a Banach space $X$ to a Banach space $Y$. First, under the weak Radon–Nikodým property, we give a representation of that dual. Next, using this representation, we provide some applications to the dual spaces of $\mathcal{K}(X,Y)$ and $\mathcal{K}_{w^{*}w}(X^{*},Y)$, the space of weak$^{*}$-weakly continuous operators.
