Properties Of Subspace-hypercyclic Operators

The paper introduces the background,concept and main examples of hypercyclic operators and weakly mixing operators.We mainly tell the Birkhoff transitivity theorem and its applications of hypercyclic operator,and introduce the criterions of hypercyclic operator and weakly mixing operator.Studing the properties of subspace hypercyclic operators and subspace-weakly mixing operators are based on hypercyclic operators and weakly mixing operators.The main conclusions are following:On one hand,we show that subspace hypercyclicity is preserved under quasiconjugacy: Let T is subspace hypercyclic operator,S is also a subspace hypercyclic operator,if S is quasiconjujate to T.Some examples are given.On the other hand,we extend the Furstenberg theorem to the setting of M-weakly mixing operators.Furthermore,a M-weakly mixing criterion is established in the end of the paper.