On one-sided star partial orders on a Rickart *-ring

Publication date: 17 October 2014

Abstract: We compare some recent approaches to extending the notions of left- and right-star partial order, introduced for complex matrices in early 90-ies, to bounded linear Hilbert space operators and to certain *-rings, and discuss in more detail a version of right-star partial order on a Rickart *-ring R. Regularity of R is not presumed.

Mathematics Subject Classification ID

Partial orders, general (06A06) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05)

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