Operators whose dual has non-separable range

TL;DR

This paper characterizes when the dual of a bounded linear operator between separable Banach spaces has a non-separable range, using properties of the operator itself.

Contribution

It provides a new characterization of the non-separability of the dual operator range based on fixing properties of the original operator.

Findings

Characterization of non-separable dual ranges in terms of fixing properties

Conditions under which the dual operator's range is non-separable

Links between operator properties and dual space structure

Abstract

Let $X$ and $Y$ be separable Banach spaces and $T:X\to Y$ be a bounded linear operator. We characterize the non-separability of $T^*(Y^*)$ by means of fixing properties of the operator $T$.