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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| Autores principales: | , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/3745d353863d4a6588c773c7f81c83c4 |
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| Sumario: | 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. |
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