Moore-Penrose inverses in rings and weighted partial isometries in C*−algebras

作者：

Highlights：

• The existence of MP-inverse in rings with involution can be used to find the optimal approximate solution of a class of linear matrix equation.

• Weighted-EP element and weighted partial isometry can be used to explore more useful results on SVD of matrices over complex numbers.

• Under some conditions, EP element and group invertible element are equivalent. An example is given to show that the equality mentioned before is not true in general.

摘要

•The existence of MP-inverse in rings with involution can be used to find the optimal approximate solution of a class of linear matrix equation.•Weighted-EP element and weighted partial isometry can be used to explore more useful results on SVD of matrices over complex numbers.•Under some conditions, EP element and group invertible element are equivalent. An example is given to show that the equality mentioned before is not true in general.

论文关键词：15A09,16U99,16W10,*−Regularity,Moore-Penrose inverse,Weighted-EP element,Weighted partial isometry,C*−algebra,

论文评审过程：Received 26 May 2018, Revised 7 June 2020, Accepted 22 November 2020, Available online 14 December 2020, Version of Record 14 December 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125832