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

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

• non-Archimedean valuation
• hypercylic operator
• supercyclic operator
• generalized backward shift operator