The Strongly (Weakly) Mixing Semigroup On Banach Spaces

In this thesis we mainly study the existence of the strongly（weakly）mixingsemi-group on Banach Spaces and the equivalence of strong and weak limits in definitionof the generator of generalized C－semi-groups and some properties relative to thegenerator.The paper is divided into four parts.In the first part,the author introductions the definition ofC₀-semi-group and theweakly mixingC₀-semi-group.And existence problem of the weakly mixingC₀-semi-group on Banach Space are studied by the Schauder basis and basis sequence.In the second part,the author introductions the definition of generalizedC₀-semi-group and its generative element is defined,and introducts some properties ofits generator;the author recall the definition of the strongly mixing generalizedC₀-semi-group. It is shown that every separable infinite dimensional complex BanachSpace admits a strongly mixing generalizedC₀-semi-group.In the third part,the author introductions the definition of C_semi-group and itsgenerative element is defined;the author recall the definition of the strongly mixingC_semi-group;it is shown that every separable infinite dimensional complex BanachSpace admits a strongly mixing generalized C_semi-group.In the fourth part,the author recall the definition of generalizedC_semi-group.Then,the paper gives a generalized C_semi-group generator and itsweak generative element is defined;it is shown that the weak equivalence,furtherdiscusses some properties of it.