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Keywords: Core inverse Core partial order Partial order Moore–Penrose inverse Group inverse Spectral property a b s t r a c t The core inverse of matrix is generalized inverse which is in some sense in-between the group and Moore–Penrose inverse. In this paper a generalization of core inverse and core partial order to Hilbert space operator case is… (More)
The minus partial order linear algebraic methods have proven to be useful in the study of complex matrices. This paper extends study of minus partial orders to general rings. It is shown that the condition a < − b, where < − is the minus partial order, defines two triples of orthogonal idempotents, and thus, a decomposition of a ring into a direct sum of… (More)
The minus partial order is already known for complex matrices and bounded linear operators on Hilbert spaces. We extend this notion to Rickart rings, and thus we generalize some well-known results.