On some generalized inverses and partial orders in ∗-rings

2022/05/16 by Janko Marovt, Dijana Mosić, Marovt, Janko +3
Computer Science · Engineering · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2205.07571

openalex publication_date 2022/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a unital ring with involution. The notions of 1MP-inverse and MP1-inverse are extended from M_m,n(\mathbbC), the set of all m× n matrices over ℂ, to the set R% ^† of all Moore-Penrose invertible elements in R. We study partial orders on R^† that are induced by 1MP-inverses and MP1-inverses. We also extend to the setting of Rickart ∗ -rings the concept of another partial order, called the plus order, which has been recently introduced on the set of all bounded linear operators between Hilbert spaces. Properties of these relations are investigated and some known results are thus generalized.

Related

• 1MP and MP1 inverses and one-sided star orders in a ring with involution
• The inverse along an element in rings
• Core partial order in rings with involution
• A new class of partial orders
• Group, Moore-Penrose, core and dual core inverse in rings with involution