In this paper, having investegated some properties of closed spectral reducible operator on Banach space, we have obtained the necessary and sufficient condition for a closed operator becoming a closed spectral operat...In this paper, having investegated some properties of closed spectral reducible operator on Banach space, we have obtained the necessary and sufficient condition for a closed operator becoming a closed spectral operator. The main results are as follows: (1) Let T be a closed spectral reducible operator, then for any closed subset F of complex plane, We have (2) Let T be a closed operator, then T becomes a closed spectral operator if and only if 1. T is a spectral reducible closed decomposable operator with property (B); 2. for every α∈ρ(T), the spectral measure E(·) of R(a,T) is satisfied with the condition E({0}) =0.展开更多
文摘In this paper, having investegated some properties of closed spectral reducible operator on Banach space, we have obtained the necessary and sufficient condition for a closed operator becoming a closed spectral operator. The main results are as follows: (1) Let T be a closed spectral reducible operator, then for any closed subset F of complex plane, We have (2) Let T be a closed operator, then T becomes a closed spectral operator if and only if 1. T is a spectral reducible closed decomposable operator with property (B); 2. for every α∈ρ(T), the spectral measure E(·) of R(a,T) is satisfied with the condition E({0}) =0.
