On quasi-affine transforms of Read's operator

We show that C. J. Read's example of an operator $T$ on $\ell_1$ which does not have any non-trivial invariant subspaces is not the adjoint of an operator on a predual of $\ell_1$. Furthermore, we present a bounded diagonal operator $D$ such that even though $D^{-1}$ is unbounded, the operator $D^{-1}TD$ is a bounded operator on $\ell_1$ with invariant subspaces, and is adjoint to an operator on $c_0$.