Disjoint and simultaneously hypercyclic pseudo-shifts

Nurhan Çolakoğlu; Özgür Martin; Rebecca Sanders

doi:10.1016/j.jmaa.2022.126130

Disjoint and simultaneously hypercyclic pseudo-shifts

Nurhan Çolakoğlu, Özgür Martin^*, Rebecca Sanders

^*Corresponding author for this work

Department of Mathematics Engineering

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

Abstract

We characterize disjoint and simultaneously hypercyclic tuples of unilateral pseudo-shift operators on ℓ^p(N). As a consequence, complementing the results of Bernal and Jung, we give a characterization for simultaneously hypercyclic tuples of unilateral weighted shifts. We also give characterizations for unilateral pseudo-shifts that satisfy the Disjoint and Simultaneous Hypercyclicity Criterions. Contrary to the disjoint hypercyclicity case, tuples of weighted shifts turn out to be simultaneously hypercyclic if and only if they satisfy the Simultaneous Hypercyclicity Criterion.

Original language	English
Article number	126130
Journal	Journal of Mathematical Analysis and Applications
Volume	512
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2022.126130
Publication status	Published - 15 Aug 2022

Bibliographical note

Publisher Copyright:
© 2022 Elsevier Inc.

Funding

The first author was partially supported by Istanbul Technical University Scientific Research Project [grant no. TAB-2017-40552 ]. The second author was partially supported by Mimar Sinan Fine Arts University Scientific Research Project [grant no. BAP-2018-15 ].

Funders	Funder number
Istanbul Technical University Scientific Research Project	TAB-2017-40552
Mimar Sinan Fine Arts University	BAP-2018-15

Keywords

Disjoint hypercyclicity
Hypercyclic operators
Hypercyclic vectors
Pseudo-shifts
Weighted shifts

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10.1016/j.jmaa.2022.126130

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AU - Çolakoğlu, Nurhan

AU - Martin, Özgür

AU - Sanders, Rebecca

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N2 - We characterize disjoint and simultaneously hypercyclic tuples of unilateral pseudo-shift operators on ℓp(N). As a consequence, complementing the results of Bernal and Jung, we give a characterization for simultaneously hypercyclic tuples of unilateral weighted shifts. We also give characterizations for unilateral pseudo-shifts that satisfy the Disjoint and Simultaneous Hypercyclicity Criterions. Contrary to the disjoint hypercyclicity case, tuples of weighted shifts turn out to be simultaneously hypercyclic if and only if they satisfy the Simultaneous Hypercyclicity Criterion.

AB - We characterize disjoint and simultaneously hypercyclic tuples of unilateral pseudo-shift operators on ℓp(N). As a consequence, complementing the results of Bernal and Jung, we give a characterization for simultaneously hypercyclic tuples of unilateral weighted shifts. We also give characterizations for unilateral pseudo-shifts that satisfy the Disjoint and Simultaneous Hypercyclicity Criterions. Contrary to the disjoint hypercyclicity case, tuples of weighted shifts turn out to be simultaneously hypercyclic if and only if they satisfy the Simultaneous Hypercyclicity Criterion.

KW - Disjoint hypercyclicity

KW - Hypercyclic operators

KW - Hypercyclic vectors

KW - Pseudo-shifts

KW - Weighted shifts

UR - https://www.scopus.com/pages/publications/85126869003

U2 - 10.1016/j.jmaa.2022.126130

DO - 10.1016/j.jmaa.2022.126130

M3 - Article

AN - SCOPUS:85126869003

SN - 0022-247X

VL - 512

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

M1 - 126130

ER -

Disjoint and simultaneously hypercyclic pseudo-shifts

Abstract

Bibliographical note

Funding

Keywords

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