On sets of elements in Rickart rings induced by partial orders

Janko Marovt and Katja Mihelič

Applied Mathematics and Computation, 2017, vol. 315, issue C, 555-563

Abstract: Let A be a Rickart ring and let A(1) be the set of all regular elements in A. The set of all a∈A such that a ≤ b are characterized, where b∈A(1) is given and ≤ is the minus partial order. In case when A is a Rickart *-ring, such sets are characterized for the diamond, the left-star, the right-star, the left-sharp, and the right-sharp partial orders. Some recent results of Mosić et al. on partial orders in B(H), the algebra of all bounded linear operators on a Hilbert space H, are thus generalized.

Keywords: Minus partial order; Diamond partial order; One-sided partial order; Bounded linear operator; Rickart ring (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:315:y:2017:i:c:p:555-563

DOI: 10.1016/j.amc.2017.08.015

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