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.