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

2013/07/16 by Xiaoxiang Zhang, Shuangshuang Zhang, Zhang, Xiaoxiang +5
Mathematics · #15A09 #16U99 #16W10 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:15A09 #msc:16U99 #msc:16W10

paper · pdf · doi:10.48550/arxiv.1307.4142

arxiv created 2013/07/16 · arxiv updated 2013/07/17

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.

Related

• The Moore-Penrose inverse of differences and products of projectors in a ring with involution
• The Moore-Penrose inverse in rings with involution
• Characterizations of core and dual core inverses in rings with involution
• Group, Moore-Penrose, core and dual core inverse in rings with involution
• Products of orthogonal projections and polar decompositions