Banach Journal of Mathematical Analysis

On star, sharp, core, and minus partial orders in Rickart rings

Janko Marovt

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Abstract

Let A be a Rickart *-ring and let *,,, and denote the star, the sharp, the core, and the dual core partial orders in A, respectively. The sets of all bA such that ab, along with the sets of all bA such that ba, are characterized, where aA 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 A are also studied. Some recent results of Cvetković-Ilić et al. on partial orders in B(H), the algebra of all bounded linear operators on a Hilbert space H, are thus generalized.

Article information

Source
Banach J. Math. Anal., Volume 10, Number 3 (2016), 495-508.

Dates
Received: 29 May 2015
Accepted: 21 October 2015
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1465230960

Digital Object Identifier
doi:10.1215/17358787-3607090

Mathematical Reviews number (MathSciNet)
MR3509881

Zentralblatt MATH identifier
1351.16038

Subjects
Primary: 47C10: Operators in $^*$-algebras
Secondary: 06F25: Ordered rings, algebras, modules {For ordered fields, see 12J15; see also 13J25, 16W80} 06A06: Partial order, general 15A09: Matrix inversion, generalized inverses

Keywords
star partial order sharp partial order core partial order bounded linear operator Rickart ring

Citation

Marovt, Janko. On star, sharp, core, and minus partial orders in Rickart rings. Banach J. Math. Anal. 10 (2016), no. 3, 495--508. doi:10.1215/17358787-3607090. https://projecteuclid.org/euclid.bjma/1465230960


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References

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