  We present a general method for constructing operators without non-trivial
invariant closed subsets on a large class of non-reflexive Banach spaces. In
particular, our approach unifies and generalizes several constructions due to
Read of operators without non-trivial invariant subspaces on the spaces
$\ell_{1}$, $c_{0}$ or $\oplus_{\ell_{2}}J$, and without non-trivial invariant
subsets on $\ell_{1}$. We also investigate how far our methods can be extended
to the Hilbertian setting, and construct an operator on a quasireflexive dual
Banach space which has no non-trivial $w^{*}$-closed invariant subspace.
