Supercyclic and Hypercyclic Generalized Weighted Backward Shifts over a Non-Archimedean <inline-formula><math display="inline"><semantics><mrow><msub><mi>c</mi><mn>0</mn></msub><mrow><mo>(</mo><mi mathvariant="double-struck">N</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> Space
In the present paper, we propose to study generalized weighted backward shifts <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>B</mi><mi mathvariant="script">B</mi><...
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oai:doaj.org-article:3745d353863d4a6588c773c7f81c83c42021-11-25T18:17:49ZSupercyclic and Hypercyclic Generalized Weighted Backward Shifts over a Non-Archimedean <inline-formula><math display="inline"><semantics><mrow><msub><mi>c</mi><mn>0</mn></msub><mrow><mo>(</mo><mi mathvariant="double-struck">N</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> Space10.3390/math92229862227-7390https://doaj.org/article/3745d353863d4a6588c773c7f81c83c42021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2986https://doaj.org/toc/2227-7390In the present paper, we propose to study generalized weighted backward shifts <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>B</mi><mi mathvariant="script">B</mi></msub></semantics></math></inline-formula> over non-Archimedean <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>c</mi><mn>0</mn></msub><mrow><mo>(</mo><mi mathvariant="double-struck">N</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> spaces; here, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">B</mi><mo>=</mo><mo>(</mo><msub><mi>b</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>)</mo></mrow></semantics></math></inline-formula> is an upper triangular matrix with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo movablelimits="true" form="prefix">sup</mo><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mrow><mo>|</mo><msub><mi>b</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>|</mo></mrow><mo><</mo><mo>∞</mo></mrow></semantics></math></inline-formula>. We investigate the sypercyclic and hypercyclic properties of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>B</mi><mi mathvariant="script">B</mi></msub></semantics></math></inline-formula>. Furthermore, certain properties of the operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mo>+</mo><msub><mi>B</mi><mi mathvariant="script">B</mi></msub></mrow></semantics></math></inline-formula> are studied as well. To establish the hypercyclic property of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mo>+</mo><msub><mi>B</mi><mi mathvariant="script">B</mi></msub></mrow></semantics></math></inline-formula> we have essentially used the non-Archimedeanity of the norm which leads to the difference between the real case.Farrukh MukhamedovOtabek KhakimovAbdessatar SouissiMDPI AGarticlenon-Archimedean valuationhypercylic operatorsupercyclic operatorgeneralized backward shift operatorMathematicsQA1-939ENMathematics, Vol 9, Iss 2986, p 2986 (2021) |
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non-Archimedean valuation hypercylic operator supercyclic operator generalized backward shift operator Mathematics QA1-939 |
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non-Archimedean valuation hypercylic operator supercyclic operator generalized backward shift operator Mathematics QA1-939 Farrukh Mukhamedov Otabek Khakimov Abdessatar Souissi Supercyclic and Hypercyclic Generalized Weighted Backward Shifts over a Non-Archimedean <inline-formula><math display="inline"><semantics><mrow><msub><mi>c</mi><mn>0</mn></msub><mrow><mo>(</mo><mi mathvariant="double-struck">N</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> Space |
| description |
In the present paper, we propose to study generalized weighted backward shifts <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>B</mi><mi mathvariant="script">B</mi></msub></semantics></math></inline-formula> over non-Archimedean <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>c</mi><mn>0</mn></msub><mrow><mo>(</mo><mi mathvariant="double-struck">N</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> spaces; here, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">B</mi><mo>=</mo><mo>(</mo><msub><mi>b</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>)</mo></mrow></semantics></math></inline-formula> is an upper triangular matrix with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo movablelimits="true" form="prefix">sup</mo><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mrow><mo>|</mo><msub><mi>b</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>|</mo></mrow><mo><</mo><mo>∞</mo></mrow></semantics></math></inline-formula>. We investigate the sypercyclic and hypercyclic properties of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>B</mi><mi mathvariant="script">B</mi></msub></semantics></math></inline-formula>. Furthermore, certain properties of the operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mo>+</mo><msub><mi>B</mi><mi mathvariant="script">B</mi></msub></mrow></semantics></math></inline-formula> are studied as well. To establish the hypercyclic property of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mo>+</mo><msub><mi>B</mi><mi mathvariant="script">B</mi></msub></mrow></semantics></math></inline-formula> we have essentially used the non-Archimedeanity of the norm which leads to the difference between the real case. |
| format |
article |
| author |
Farrukh Mukhamedov Otabek Khakimov Abdessatar Souissi |
| author_facet |
Farrukh Mukhamedov Otabek Khakimov Abdessatar Souissi |
| author_sort |
Farrukh Mukhamedov |
| title |
Supercyclic and Hypercyclic Generalized Weighted Backward Shifts over a Non-Archimedean <inline-formula><math display="inline"><semantics><mrow><msub><mi>c</mi><mn>0</mn></msub><mrow><mo>(</mo><mi mathvariant="double-struck">N</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> Space |
| title_short |
Supercyclic and Hypercyclic Generalized Weighted Backward Shifts over a Non-Archimedean <inline-formula><math display="inline"><semantics><mrow><msub><mi>c</mi><mn>0</mn></msub><mrow><mo>(</mo><mi mathvariant="double-struck">N</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> Space |
| title_full |
Supercyclic and Hypercyclic Generalized Weighted Backward Shifts over a Non-Archimedean <inline-formula><math display="inline"><semantics><mrow><msub><mi>c</mi><mn>0</mn></msub><mrow><mo>(</mo><mi mathvariant="double-struck">N</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> Space |
| title_fullStr |
Supercyclic and Hypercyclic Generalized Weighted Backward Shifts over a Non-Archimedean <inline-formula><math display="inline"><semantics><mrow><msub><mi>c</mi><mn>0</mn></msub><mrow><mo>(</mo><mi mathvariant="double-struck">N</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> Space |
| title_full_unstemmed |
Supercyclic and Hypercyclic Generalized Weighted Backward Shifts over a Non-Archimedean <inline-formula><math display="inline"><semantics><mrow><msub><mi>c</mi><mn>0</mn></msub><mrow><mo>(</mo><mi mathvariant="double-struck">N</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> Space |
| title_sort |
supercyclic and hypercyclic generalized weighted backward shifts over a non-archimedean <inline-formula><math display="inline"><semantics><mrow><msub><mi>c</mi><mn>0</mn></msub><mrow><mo>(</mo><mi mathvariant="double-struck">n</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> space |
| publisher |
MDPI AG |
| publishDate |
2021 |
| url |
https://doaj.org/article/3745d353863d4a6588c773c7f81c83c4 |
| work_keys_str_mv |
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