保持拟可逆性或拟零因子的可加映射

宋显花, 吉国兴

数学学报 ›› 2017, Vol. 60 ›› Issue (2) : 217-230.

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数学学报 ›› 2017, Vol. 60 ›› Issue (2) : 217-230. DOI: 10.12386/A2017sxxb0018
论文

保持拟可逆性或拟零因子的可加映射

    宋显花1,2, 吉国兴1
作者信息 +

Additive Maps Preserving Quasi-invertibilities or Quasi-zero Divisors

    Xian Hua SONG1,2, Guo Xing JI1
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文章历史 +

摘要

XY是维数大于1的复Banach空间,AB分别是BX)和BY)中包含有限秩算子的范数闭子代数.∀ABA,定义AB=A+B-AB,称A,B的拟积.刻画了从AB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.

Abstract

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, BA, we define the quasi-product of A and B as AB=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.

关键词

算子代数 / 拟可逆性 / 拟零因子 / 同构

Key words

operator algebras / quasi-invertibility / quasi-zero divisors / isomorphisms

引用本文

导出引用
宋显花, 吉国兴. 保持拟可逆性或拟零因子的可加映射. 数学学报, 2017, 60(2): 217-230 https://doi.org/10.12386/A2017sxxb0018
Xian Hua SONG, Guo Xing JI. Additive Maps Preserving Quasi-invertibilities or Quasi-zero Divisors. Acta Mathematica Sinica, Chinese Series, 2017, 60(2): 217-230 https://doi.org/10.12386/A2017sxxb0018

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基金

国家自然科学基金资助项目(11371233);中央高校基本科研业务费专项资金(GK201301007)

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