N-multiple Nonwandering Unilateral Weighted Backward Shift Operators and the Property of Direct Sum Operators in Banach Space

In this paper,we take the methods of differential dynamics and basic theories of the operator as tools on the basis of hypercyclicity chaos of operator,and do further research on the nonwandering property of the operator.In infinite dimensional separable Banach space,we have known the nonwandering operators,which are linear ones of chaotic character.We introduce n-multiple non- wandering operators.Firstly,we give the definition of n-multiple nonwander- ing operator.Then,by the method of function analysis,we prove that in separable Banach space unilateral weighted backward shifts operators are n-multiple nonwandering operators.Also,we obtain that the direct sum operator of the finite nonwandering operators are n-multiple nonwan- dering operators.