Recurrent Linear Operators
By George Costakis, Antonios Manoussos, Ioannis Parissis. 2013
73 citations recorded by the source corpus.
We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication operators on classical Banach spaces. We show that on separable complex Hilbert spaces the study of recurrent operators reduces, in many cases, to the study of unitary operators. Finally, we study the notion of product recurrence and state some relevant open questions.
Subfields: Algebra and Number Theory, Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/e9be6920481d85ebc74d87b05371e4029d31d636
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In Algebra and Number Theory
- S. Grivaux
- Alfredo Peris
- Antonio Bonilla
- É. Matheron
- K. Grosse-Erdmann
- Antoni L'opez-Mart'inez
- Quentin Menet
- Fr'ed'eric Bayart
In Applied Mathematics
- S. Grivaux
- Alfredo Peris
- É. Matheron
- Antonio Bonilla
- K. Grosse-Erdmann
- Quentin Menet
- Antoni L'opez-Mart'inez
- Fr'ed'eric Bayart
Citations in the corpus
- Frequently recurrent operators (2020, background): “If T is recurrent, the set of recurrent vectors for T is residual, see [19].”
- Invariant measures for frequently hypercyclic operators (2014, background): “In the linear setting, it has been more particularly studied recently in [11].”