Supercyclic and hypercyclic generalized weighted backward shifts over a non-archimedean c0(N) space

Farrukh Mukhamedov; Otabek Khakimov; Abdessatar Souissi

doi:10.3390/math9222986

Supercyclic and hypercyclic generalized weighted backward shifts over a non-archimedean c₀(N) space

Farrukh Mukhamedov, Otabek Khakimov, Abdessatar Souissi

Department of Mathematical Sciences

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

Abstract

In the present paper, we propose to study generalized weighted backward shifts B_B over non-Archimedean c₀ (N) spaces; here, B = (b_ij) is an upper triangular matrix with sup_i,j |b_ij | < ∞. We investigate the sypercyclic and hypercyclic properties of B_B. Furthermore, certain properties of the operator I + B_B are studied as well. To establish the hypercyclic property of I + B_B we have essentially used the non-Archimedeanity of the norm which leads to the difference between the real case.

Original language	English
Article number	2986
Journal	Mathematics
Volume	9
Issue number	22
DOIs	https://doi.org/10.3390/math9222986
Publication status	Published - Nov 1 2021

Keywords

Generalized backward shift operator
Hypercylic operator
Non-Archimedean valuation
Supercyclic operator

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.3390/math9222986

Cite this

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title = "Supercyclic and hypercyclic generalized weighted backward shifts over a non-archimedean c0(N) space",

abstract = "In the present paper, we propose to study generalized weighted backward shifts BB over non-Archimedean c0 (N) spaces; here, B = (bij) is an upper triangular matrix with supi,j |bij | < ∞. We investigate the sypercyclic and hypercyclic properties of BB. Furthermore, certain properties of the operator I + BB are studied as well. To establish the hypercyclic property of I + BB we have essentially used the non-Archimedeanity of the norm which leads to the difference between the real case.",

keywords = "Generalized backward shift operator, Hypercylic operator, Non-Archimedean valuation, Supercyclic operator",

author = "Farrukh Mukhamedov and Otabek Khakimov and Abdessatar Souissi",

note = "Funding Information: Acknowledgments: The first named author (F.M.) thanks to the UAEU UPAR Grant No. G00003247 for support. The authors are grateful to all referees for their useful suggestions which allowed to improve the presentation of this paper. Funding Information: Funding: The present work is supported by the UAEU UPAR Grant No. 31S391). Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland.",

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N2 - In the present paper, we propose to study generalized weighted backward shifts BB over non-Archimedean c0 (N) spaces; here, B = (bij) is an upper triangular matrix with supi,j |bij | < ∞. We investigate the sypercyclic and hypercyclic properties of BB. Furthermore, certain properties of the operator I + BB are studied as well. To establish the hypercyclic property of I + BB we have essentially used the non-Archimedeanity of the norm which leads to the difference between the real case.

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