在无穷维可分Banach空间中引进了无环条件和滤子的概念,给出了非游荡算子的滤子的例子,说明了基本集满足无环条件的非游荡算子是存在的,在此基础上给出了非游荡算子的拓扑稳定性定理。
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.