Banach Journal of Mathematical Analysis

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

Janko Marovt

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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