A note on non-supercyclic vectors of Hilbert space operators

In this note it is shown that there is a bounded linear operator T on the Hardy Hilbert space H2 and a vector f in H2 such that the closure of the set {αTnf:α∈ℂ,n≥0} is not H2, but for every subsequence (nk)k=1∞ the closed linear span of {Tnkf:k≥1} is the whole space H2. Furthermore, the closure of...

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Published inExamples and counterexamples Vol. 5; p. 100131
Main Authors Faghih-Ahmadi, Masoumeh, Hedayatian, Karim
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2024
Elsevier
Subjects
Composition operators
Hardy spaces
Non-supercyclic vectors
secondary
Non-supercyclic vectors
Composition operators
Hardy spaces
primary
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Summary:In this note it is shown that there is a bounded linear operator T on the Hardy Hilbert space H2 and a vector f in H2 such that the closure of the set {αTnf:α∈ℂ,n≥0} is not H2, but for every subsequence (nk)k=1∞ the closed linear span of {Tnkf:k≥1} is the whole space H2. Furthermore, the closure of {Tng:n≥0} is H2 for some g∈H2.
ISSN:2666-657X
2666-657X
DOI:10.1016/j.exco.2023.100131