Relationships between DMP relation and some partial orders

Chunyuan Deng and Anqi Yu

Applied Mathematics and Computation, 2015, vol. 266, issue C, 41-53

Abstract: Let H be an infinite-dimensional complex Hilbert space and let B(H) be the algebra of all bounded linear operators on H. The equivalent definition of the DMP relation on B(H), using operator block matrices, is introduced. We present a new interpretation of this relation which allows to generalize many known results for matrices to general Hilbert spaces regarding the DMP relation and its relationship with the star order and minus partial order. Also some properties of DMP relation, defined with the help of idempotent operators, are investigated.

Keywords: DMP inverse; Projection; Star partial order; Minus partial order (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:266:y:2015:i:c:p:41-53

DOI: 10.1016/j.amc.2015.05.023

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