This is an announcement for the paper "A general approach to Read's type constructions of operators without non-trivial invariant closed subspaces" by Sophie Grivaux and Maria Roginskaya.

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 $w^{*}$-closed invariant subspace.

Archive classification: math.FA

Remarks: 62 p

Submitted from: grivaux@math.univ-lille1.fr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1301.6143

or

http://arXiv.org/abs/1301.6143