This is an announcement for the paper "Localizing algebras and invariant subspaces" by Miguel Lacruz and Luis Rodriguez-Piazza.

Abstract: It is shown that the algebra (L^\infty(\mu)) of all bounded measurable functions with respect to a finite measure (\mu) is localizing on the Hilbert space (L^2(\mu)) if and only if the measure (\mu) has an atom. Next, it is shown that the algebra (H^\infty({\mathbb D})) of all bounded analytic multipliers on the unit disc fails to be localizing, both on the Bergman space (A^2({\mathbb D})) and on the Hardy space (H^2({\mathbb D}).) Then, several conditions are provided for the algebra generated by a diagonal operator on a Hilbert space to be localizing. Finally, a theorem is provided about the existence of hyperinvariant subspaces for operators with a localizing subspace of extended eigenoperators. This theorem extends and unifies some previously known results of Scott Brown and Kim, Moore and Pearcy, and Lomonosov, Radjavi and Troitsky.

Archive classification: math.OA

Mathematics Subject Classification: 47L10, 47A15

Remarks: 15 pages, submitted to J. Operator Theory

Submitted from: lacruz@us.es

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

http://front.math.ucdavis.edu/1308.4995

or

http://arXiv.org/abs/1308.4995