Abstract:

The stability of a non-wandering operator is studied by introducing filtration and nocycle condition in infinite dimensional separable Banach space. Some examples of filtration and no-cycle condition in infinite dimensional separable Banach space are shown. Then a sufficient condition for a non-wandering vector manifold to be stable is given.
 

Key words: non-wandering operator; hyper-cyclic operator; filtration; no-cycle condition; topologically stability