This is an announcement for the paper “Banach spaces and operators with non-separable dual” by Philip A.H. Brookerhttps://arxiv.org/find/math/1/au:+Brooker_P/0/1/0/all/0/1.
Abstract: Let $W$ and $Z$ be Banach spaces such that $Z$ is separable and let $R: W\rightarrow Z$ be a (continuous, linear) operator. We study consequences of the adjoint operator $R^*$ having non-separable range. From our main technical result we obtain applications to the theory of basic sequences and the existence of universal operators for various classes of operators between Banach spaces. We also obtain an operator-theoretic characterisation of separable Banach spaces with non-separable dual.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1612.08130