Hypercyclic Operator In C₀(N) And C₀(Z) Space

With the development of linear operator hypercyclic theory, We get some equivalent conditions about weighted sequence, on which weighted shift operator in l²(N) and l²(Z) become hypercyclic. The researchers hope to study the hypercyclic operator in more general space. So next we study the weighted shift hypercyclic operator in c₀( N ) space and c₀(Z) space and get some properties of its weighted sequence.In this paper, we first give an example that the bilateral weighted shift operator in c₀(Z)space is hypercyclic operator and first solve the existence problem of hypercyclic operator in c₀( N )(or c₀(Z)) space . And then we investigate the property of weighted shift operator in c₀(Z) space and an important property of the hypercyclic vector of weighted shift operator in c₀( N ) space and c₀(Z) space. At last we give the concept of weak hypercyclic operator and weak hypercyclic vector , and give the equivalence between the weak hypercyclicity and the hypercyclicity in l¹(N) space.