Banach空间上的左可逆算子的稳定性

THE STABILITY OF THE LEFT INVERTIBLE OPERATORS IN BANACH SPACE

主要讨论了 Banach空间上左可逆算子在线性运算下的稳定性及一些摄动问题 ,并通过反例证明了对于 Banach空间上的左可逆算子 A和 B,R(A)∩ R(B) ={0 }不是 λA+B( λ∈C)为左可逆算子的必要条件 .

The stability of the left invertible operators under the linear operation and some perturbation questions are discussed in this paper,and an example is given to explain that R(A)∩R(B)={0} is not necessary so that λA+B is also a left invertible operator for λ∈C when A and B are left invertible