Journal of Operator Theory
Volume 73, Issue 2, Spring 2015 pp. 385-405.
Hereditarily hypercyclic subspaces
Authors:
Quentin Menet
Author institution:Institut de Mathematique,
Universite de Mons,
20 Place du Parc,
7000 Mons, Belgique
Summary: We say that a sequence of operators $(T_n)$ possesses hereditarily hypercyclic subspaces along a sequence $(n_k)$ if for any subsequence $(m_k)\subset(n_k)$, the sequence $(T_{m_k})$ possesses a hypercyclic subspace. While so far no characterization of the existence of hypercyclic subspaces in the case of Fr\'{e}chet spaces is known, we succeed to obtain a characterization of sequences $(T_n)$ possessing hereditarily hypercyclic subspaces along $(n_k)$, under the assumption that the sequence $(T_n)$ satisfies the hypercyclicity criterion along $(n_k)$.
We also obtain a characterization of operators possessing a hypercyclic subspace under the assumption that $T$ satisfies the frequent hypercyclicity criterion.
DOI: http://dx.doi.org/10.7900/jot.2013dec20.2012
Keywords: hypercyclic operators, hypercyclic subspaces
Contents
Full-Text PDF