This is an announcement for the paper "A complete locally convex space of countable dimension admitting an operator with no invariant subspaces" by Stanislav Shkarin.

Abstract: We construct a complete locally convex topological vector space $X$ of countable algebraic dimension and a continuous linear operator $T:X\to X$ such that $T$ has no non-trivial closed invariant subspaces.

Archive classification: math.FA

Mathematics Subject Classification: 47A16

Submitted from: s.shkarin@qub.ac.uk

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

http://front.math.ucdavis.edu/1009.2644

or

http://arXiv.org/abs/1009.2644