Abstract
Let be a Rickart -ring and let , and denote the star, the sharp, the core, and the dual core partial orders in , respectively. The sets of all such that , along with the sets of all such that , are characterized, where is given and where is one of the partial orders: , or , or , or . Such sets of elements that are above or below a given element under the minus partial order in a Rickart ring are also studied. Some recent results of Cvetković-Ilić et al. on partial orders in , the algebra of all bounded linear operators on a Hilbert space , are thus generalized.
Citation
Janko Marovt. "On star, sharp, core, and minus partial orders in Rickart rings." Banach J. Math. Anal. 10 (3) 495 - 508, July 2016. https://doi.org/10.1215/17358787-3607090
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