Natural structures on semigroups with involution

Drazin, M. P.

doi:10.1090/s0002-9904-1978-14442-5

Cited by 207 publications

(105 citation statements)

References 5 publications

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101

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Order By: Relevance

“…There are several characterizations of the ordering , e.g., A B if and only if AB = A 2 . This shows that is the restriction of D r a z i n 's order ( [4]) from the set B(H) of all bounded operators on H, to the self-adjoint part S(H). Indeed, the Drazin order a ≤ d b is introduced by the binary relation a * a = a * b = b * a and aa * = ab * = ba * .…”

Section: Shows That (S(h) ≤) Is Not a Lattice It Is Even An Antilatmentioning

confidence: 92%

Remarks on the order for quantum observables

Pulmannová

Vinceková

2007

Mathematica Slovaca

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ABSTRACT. Relations between generalized effect algebras and the sets of classical and quantum observables endowed with an ordering recently introduced in [GUDDER, S.: An order for quantum observables, Math. Slovaca 56 (2006), 573-589] are studied. In the classical case, a generalized OMP, while in the quantum case a weak generalized OMP is obtained. Existence of infima for arbitrary sets and suprema for above bounded sets in the quantum case is shown. Compatibility in the sense of Mackey is characterized.

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Section: Shows That (S(h) ≤) Is Not a Lattice It Is Even An Antilatmentioning

confidence: 92%

Remarks on the order for quantum observables

Pulmannová

Vinceková

2007

Mathematica Slovaca

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“…The star partial order, denoted by ≤ * , was introduced by Drazin in [13] and it has been widely studied in the literature. In [1], Baksalary et al studied certain partial orders on complex matrices and some relationships with their powers.…”

Section: Introductionmentioning

confidence: 99%

The star partial order and the eigenprojection at 0 on EP matrices

Hernández

Lattanzi

Thome

et al. 2012

Applied Mathematics and Computation

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The star partial order and the eigenprojection at 0 on EPThe space of n × n complex matrices with the star partial order is considered in the first part of this paper. The class of EP matrices is analyzed and several properties related to this order are given. In addition, some information about predecessors and successors of a given EP matrix is obtained. The second part is dedicated to the study of some properties that relate the eigenprojection at 0 with the star and sharp partial orders.

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“…One of them, the star ordering, was introduced by Drazin in [4] in the following way: If A, B ∈ C n×m , then…”

Section: The Star Partial Orderingmentioning

confidence: 99%