A general approach to Read's type constructions of operators without non-trivial invariant closed subspaces
Artikel i vetenskaplig tidskrift, 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.

Banach-Spaces

Reflexitivity

Mathematics

Författare

S. Grivaux

CNRS Centre National de la Recherche Scientifique

Maria Roginskaya

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Proceedings of the London Mathematical Society

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

Vol. 109 596-652

Ämneskategorier

Matematik

DOI

10.1112/plms/pdu012