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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    ℓ  1   ,    c  0    or⨁   ℓ  2    J   , and without non‐trivial invariant subsets on    ℓ  1   . We also investigate how far our methods can be extended to the Hilbertian setting, and construct an operator on a quasi‐reflexive dual Banach space which has no non‐trivial    w  *   ‐closed invariant subspace.

A general approach to Read's type constructions of operators without non‐trivial invariant closed subspaces