left invertible element

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 invertibl

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 。