Numerically Hypercyclic Operators

Sung Guen Kim; Alfredo Peris; Hyun Gwi Song

doi:10.1007/s00020-012-1944-1

Numerically Hypercyclic Operators

Sung Guen Kim, Alfredo Peris, Hyun Gwi Song

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

5 Scopus citations

Abstract

An operator T acting on a normed space E is numerically hypercyclic if, for some (x, x ^*) ∈ Π(E), the numerical orbit {x ^*(T ⁿ(x)): n ≥ 0} is dense in ℂ. We prove that finite dimensional Banach spaces with dimension at least two support numerically hypercyclic operators. We also characterize the numerically hypercyclic weighted shifts on classical sequence spaces.

Original language	English
Pages (from-to)	393-402
Number of pages	10
Journal	Integral Equations and Operator Theory
Volume	72
Issue number	3
DOIs	https://doi.org/10.1007/s00020-012-1944-1
State	Published - Mar 2012

Keywords

Numerically hypercyclic operators
weighted shift operators

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10.1007/s00020-012-1944-1

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title = "Numerically Hypercyclic Operators",

abstract = "An operator T acting on a normed space E is numerically hypercyclic if, for some (x, x *) ∈ Π(E), the numerical orbit {x *(T n(x)): n ≥ 0} is dense in ℂ. We prove that finite dimensional Banach spaces with dimension at least two support numerically hypercyclic operators. We also characterize the numerically hypercyclic weighted shifts on classical sequence spaces.",

keywords = "Numerically hypercyclic operators, weighted shift operators",

author = "Kim, {Sung Guen} and Alfredo Peris and Song, {Hyun Gwi}",

year = "2012",

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doi = "10.1007/s00020-012-1944-1",

language = "English",

volume = "72",

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journal = "Integral Equations and Operator Theory",

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AU - Kim, Sung Guen

AU - Peris, Alfredo

AU - Song, Hyun Gwi

PY - 2012/3

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N2 - An operator T acting on a normed space E is numerically hypercyclic if, for some (x, x *) ∈ Π(E), the numerical orbit {x *(T n(x)): n ≥ 0} is dense in ℂ. We prove that finite dimensional Banach spaces with dimension at least two support numerically hypercyclic operators. We also characterize the numerically hypercyclic weighted shifts on classical sequence spaces.

AB - An operator T acting on a normed space E is numerically hypercyclic if, for some (x, x *) ∈ Π(E), the numerical orbit {x *(T n(x)): n ≥ 0} is dense in ℂ. We prove that finite dimensional Banach spaces with dimension at least two support numerically hypercyclic operators. We also characterize the numerically hypercyclic weighted shifts on classical sequence spaces.

KW - Numerically hypercyclic operators

KW - weighted shift operators

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U2 - 10.1007/s00020-012-1944-1

DO - 10.1007/s00020-012-1944-1

M3 - Article

AN - SCOPUS:84862786374

SN - 0378-620X

VL - 72

SP - 393

EP - 402

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 3

ER -

Numerically Hypercyclic Operators

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