The D-hypercyclicity Of Weighted Shifts On Weighted Sequence Spaces

In this paper,we characterize the d-hypercyclicity of finitely many different powers of weighted shifts acting on the weighted sequence spaces l2(N,?),C0(N,?)and l2(Z,?),C0(Z,?).It is discussed from the following chapters.In chaper 1,we mainly introduces the research background,some current situation of domestic and foreign research,and some unsolved problems,and then state the content of our dissertation.In chaper 2,first,we introduce some basic definitions and several important theorems;Then we introduced two important criteria:Hypercyclicity Criterion and d-Hypercyclicity Criterion;Finally,we give a detailed introduction to the shift operators,and give some existing conclusions.In chaper 3,We further study the d-hypercyclic properties of shift operators.The main conclusions are following:we characterize the d-hypercyclicity of unilateral(bilat-eral)weighted shifts acting on the weighted sequence spaces l2(N,?)C0(N,?)and l2(Z,?),C0(Z,?)and several equivalent depictions.In the final charpter,we summarize the main results of the thesis,and give an outlook for future research.