Moore-Penrose Invertibility of Differences and Products of Projections in Rings with Involution

Xiaoxiang Zhang; Shuangshuang Zhang; Jianlong Chen; Long Wang

Moore-Penrose Invertibility of Differences and Products of Projections in Rings with Involution

Rings and Algebras 2013-07-17 v1

Authors: Xiaoxiang Zhang , Shuangshuang Zhang , Jianlong Chen , Long Wang

Abstract

This article concerns the MP inverse of the differences and the products of projections in a ring $R$ with involution. Some equivalent conditions are obtained. As applications, the MP invertibility of the commutator $pq-qp$ and the anti-commutator $pq+qp$ are characterized, where $p$ and $q$ are projections in $R$ . Some related known results in $C^*$ -algebra are generalized.

Keywords

moore-penrose inverse rings with involution projections commutator anti-commutator c*-algebra

Cite

@article{arxiv.1307.4142,
  title  = {Moore-Penrose Invertibility of Differences and Products of Projections in Rings with Involution},
  author = {Xiaoxiang Zhang and Shuangshuang Zhang and Jianlong Chen and Long Wang},
  journal= {arXiv preprint arXiv:1307.4142},
  year   = {2013}
}

Moore-Penrose Invertibility of Differences and Products of Projections in Rings with Involution

Abstract

Keywords

Cite

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