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

1 Citation (Scopus)

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

Computer Science (miscellaneous)
Engineering (miscellaneous)
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",

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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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