Irregular vectors of Hilbert space operators

A vector x in a Hilbert space H is called irregular for an operator T : H → H provided that sup n ‖ T n x ‖ = ∞ and inf n ‖ T n x ‖ = 0 . We establish some basic properties of operators having irregular vectors and present examples that highlight the relationship, or lack thereof, between irregulari...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2009-06, Vol.354 (2), p.689-697
Main Author: PRAJITURA, Gabriel T
Format: Article
Language:English
Subjects:
Exact sciences and technology
Functional analysis
Hypercyclic
Irregular
Mathematical analysis
Mathematics
Operator
Orbit
Sciences and techniques of general use
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Summary:A vector x in a Hilbert space H is called irregular for an operator T : H → H provided that sup n ‖ T n x ‖ = ∞ and inf n ‖ T n x ‖ = 0 . We establish some basic properties of operators having irregular vectors and present examples that highlight the relationship, or lack thereof, between irregularity and hypercyclicity.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2009.01.034