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

Abstract

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 $w^{\ast }$-closed invariant subspace.

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Cited by in corpus (2)

• Linear Dynamical Systems
• Invariant subspaces for non-normable Fréchet spaces