Nonwandering Operator In Infinite Dimensional Separable Fréchet Space

This paper studies the nonwandering operator in infinite dimensional separable Frechet space with the methods in functional analysis and in infinite dimensional dynamic system, we give the definition of nonwandering operator in infinite separable Frechet space and prove that each infinite separable Frechet sequence space supports a nonwandering operator, and also present a concrete nonwandering operators in physical backgroud. Nonwandering operator has several propositions such as the characteristic of spectrum of it and the hypercyclic decomposition of it. Local spectral theory studies the decomposition of linear operator. Appling it we give the condition onφsuch thatφ(T) is a nonwandering operator, whereφis a analytic(or holomorphic) function on some neighborhood of the spectrum of linear operator T.