A general approach to Read's type constructions of operators without non-trivial invariant closed subspaces (Q2922877)

In this very interesting work, the authors present a general method for constructing operators without non-trivial invariant closed subsets on a large class of non-reflexive Banach spaces. In particular, their approach clarifies, unifies and generalizes several constructions due to C. Read of operators without non-trivial invariant subspaces on the spaces \(\ell_1\), \(c_0\) or \(\bigoplus_{\ell_2} J\), where \(J\) denotes the James space, and without non-trivial invariant subsets on \(\ell_1\). They show how all the known counterexamples to the invariant subspace or subset problem can be derived from a single general statement. Furthermore, they explore which geometric properties of a Banach space will ensure that it supports an operator without non-trivial invariant closed subset and they investigate how far their methods can be extended to the Hilbert space setting.