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
In this paper,we prove the Mohebi-Radjabalipour Conjecture under an ad-ditional condition,and obtain an invariant subspace theorem on subdecomposableoperators.
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.
文摘In this paper,we prove the Mohebi-Radjabalipour Conjecture under an ad-ditional condition,and obtain an invariant subspace theorem on subdecomposableoperators.
