保持拟可逆性或拟零因子的可加映射

Additive Maps Preserving Quasi-invertibilities or Quasi-zero Divisors

设X和Y是维数大于1的复Banach空间,A和B分别是B(X)和B(Y)中包含有限秩算子的范数闭子代数.A,B∈A,定义A。B=A+B-AB,称。为A,B的拟积.刻画了从A到B的双边保持算子的(左,右)拟可逆性或(左,右,半)拟零因子的可加满射的结构.

Let X, Y be complex Banach spaces with dimentions greater than 1. Let A,B be normed closed subalgebras of B（X）, B（Y） containing finite rank operators, respectively. For any A, B ∈A, we define the quasi-product of A and B as A o B =A ＋ B - AB. In this paper, A characterization of additive mappings from A onto B which preserve any one of （left, right） quasi-invertibility and （left, right, semi） quasizero divisors in both directions is given.