New results on common properties of the products AC and BA , II
New results on common properties of the products AC and BA , II
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AC 和 BA , II 产品共同性能的新结果
DOI：
10.1002/mana.201900038
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发表时间：
2020
影响因子：
1
通讯作者：
Shifang Zhang
中科院分区：
文献类型：
--
作者：
Qingping Zeng;Kai Yan;Shifang Zhang
本文继续研究乘积在环、有界线性算子或Banach代数中的一般性质。本文证明了：（i）如果酉结合环中的元素满足，则vonNeumann正则性（分别为）。广义Fredholmness相对于理想的）转换为。(ii)如果有界线性算子满足，则和共享核和值域的公共可补性。(iii)如果单位半单Banach代数中的元素满足且是的迹理想，使得sockh（x），则与相对于且具有相同的抽象指标而共享公共Fredholmness。对于本原Banach代数中的B-Fredholmness也有类似的结果。
In this note, we continue to investigate common properties of the products in the setting of rings, bounded linear operators, or Banach algebras. We prove: (i) Ifare elements in a unital associative ringsatisfying, then von Neumann regularity (resp. generalized Fredholmness relative to an idealof) ofis converted into that of. (ii) Ifare bounded linear operators satisfying, thenandshare common complementability of kernels and ranges. (iii) Ifare elements in a unital semisimple Banach algebrasatisfyingandis a trace ideal ofsuch that sockh(soc, thenandshare common Fredholmness relative toand have the same abstract index. A similar result holds for B‐Fredholmness in primitive Banach algebra.