Journal of Operator Theory

Volume 54, Issue 2, Fall 2005 pp. 251-260.

Operators with common hypercyclic subspaces

Authors: R. Aron (1), J. Bes (2), F. Leon (3), and Peris. A. (4)
Author institution: (1) Department of Mathematics, Kent State University, Kent, OH 44242, USA, (2) Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA, (3) Facultad de Derecho, Universidad de Cadiz, 11402 Jerez de la Frontera, Cadiz, Spain, (4) E.T.S. Arquitectura, D. Matem\`atica Aplicada, Universitat Polit\`ecnica de Val\`encia, E-46022 Val\`encia, Spain

Summary: We provide a reasonably sufficient condition for a countable family of operators to have a common hypercyclic subspace. We also extend a result of the third author and A. Montes, thereby obtaining a common hypercyclic subspace for certain countable families of compact perturbations of operators of norm no larger than one.

Keywords: Hypercyclic vectors, subspaces, and operators; universal families.

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