On hypercyclic rank one perturbations of unitary operators

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On hypercyclic rank one perturbations of unitary operators. / Baranov, Anton; Kapustin, Vladimir; Lishanskii, Andrei.

In: Mathematische Nachrichten, Vol. 292, No. 5, 01.05.2019, p. 961-968.

Research output: Contribution to journal › Article › peer-review

Author

Baranov, Anton ; Kapustin, Vladimir ; Lishanskii, Andrei. / On hypercyclic rank one perturbations of unitary operators. In: Mathematische Nachrichten. 2019 ; Vol. 292, No. 5. pp. 961-968.

BibTeX

@article{86e7914abd054c13815ceab1983311d8,

title = "On hypercyclic rank one perturbations of unitary operators",

abstract = "Recently, S. Grivaux showed that there exists a rank one perturbation of a unitary operator in a Hilbert space which is hypercyclic. Another construction was suggested later by the first and the third authors. Here, using a functional model for rank one perturbations of singular unitary operators, we give yet another construction of hypercyclic rank one perturbation of a unitary operator. In particular, we show that any countable union of perfect Carleson sets on the circle can be the spectrum of a perturbed (hypercyclic) operator.",

keywords = "functional model, hypercyclic operator, inner function, model space, rank one perturbation",

author = "Anton Baranov and Vladimir Kapustin and Andrei Lishanskii",

year = "2019",

month = may,

day = "1",

doi = "10.1002/mana.201800242",

language = "English",

volume = "292",

pages = "961--968",

journal = "Mathematische Nachrichten",

issn = "0025-584X",

publisher = "Wiley-Blackwell",

number = "5",

}

RIS

TY - JOUR

T1 - On hypercyclic rank one perturbations of unitary operators

AU - Baranov, Anton

AU - Kapustin, Vladimir

AU - Lishanskii, Andrei

PY - 2019/5/1

Y1 - 2019/5/1

N2 - Recently, S. Grivaux showed that there exists a rank one perturbation of a unitary operator in a Hilbert space which is hypercyclic. Another construction was suggested later by the first and the third authors. Here, using a functional model for rank one perturbations of singular unitary operators, we give yet another construction of hypercyclic rank one perturbation of a unitary operator. In particular, we show that any countable union of perfect Carleson sets on the circle can be the spectrum of a perturbed (hypercyclic) operator.

AB - Recently, S. Grivaux showed that there exists a rank one perturbation of a unitary operator in a Hilbert space which is hypercyclic. Another construction was suggested later by the first and the third authors. Here, using a functional model for rank one perturbations of singular unitary operators, we give yet another construction of hypercyclic rank one perturbation of a unitary operator. In particular, we show that any countable union of perfect Carleson sets on the circle can be the spectrum of a perturbed (hypercyclic) operator.

KW - functional model

KW - hypercyclic operator

KW - inner function

KW - model space

KW - rank one perturbation

UR - http://www.scopus.com/inward/record.url?scp=85057838773&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/hypercyclic-rank-one-perturbations-unitary-operators

U2 - 10.1002/mana.201800242

DO - 10.1002/mana.201800242

M3 - Article

AN - SCOPUS:85057838773

VL - 292

SP - 961

EP - 968

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

IS - 5

ER -

ID: 42618729