A general approach to Read's type constructions of operators without non-trivial invariant closed subspaces
Journal article, 2014

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 circle plus(l2) 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.





S. Grivaux

Centre national de la recherche scientifique (CNRS)

Maria Roginskaya

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Proceedings of the London Mathematical Society

0024-6115 (ISSN) 1460-244X (eISSN)

Vol. 109 3 596-652

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