Geodesic
Commutant hypercyclicity of Hilbert space operators
Filomat, Tome 37 (2023) no. 15, p. 4857

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DOI

An operator T on a Hilbert space H is commutant hypercyclic if there is a vector x in H such that the set {Sx : TS = ST} is dense in H. We prove that operators on finite dimensional Hilbert space, a rich class of weighted shift operators, isometries, exponentially isometries and idempotents are all commutant hypercyclic. Then we discuss on commutant hypercyclicity of 2 × 2 operator matrices. Moreover, for each integer number n ≥ 2, we give a commutant hypercyclic nilpotent operator of order n on an infinite dimensional Hilbert space. Finally, we study commutant transitivity of operators and give necessary and sufficient conditions for a vector to be a commutant hypercyclic vector.
DOI : 10.2298/FIL2315857H
Classification : 47A16, 47B37, 47B99
Keywords: Commutant hypercyclicity, Operators, Hilbert spaces, Weighted shift 
Karim Hedayatian; Mohammad Namegoshayfard. Commutant hypercyclicity of Hilbert space operators. Filomat, Tome 37 (2023) no. 15, p. 4857 . doi: 10.2298/FIL2315857H
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     title = {Commutant hypercyclicity of {Hilbert} space operators},
     journal = {Filomat},
     pages = {4857 },
     year = {2023},
     volume = {37},
     number = {15},
     doi = {10.2298/FIL2315857H},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2315857H/}
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