Some results on partial ordering and reverse order law of elements of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mi>C</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:math>-algebras

Liu, Xiaoji; Benítez, Julio; Zhong, Jin

doi:10.1016/j.jmaa.2010.05.005

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Cited by 12 publications

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“…Further results on ROL for Moore‐Penrsoe inverse can be found in [13, 15, 21]. The ROL for K ‐inverses, where

K\subseteq \lbrace 1,2,3,4\rbrace

, are considered in [3, 4, 6–9, 16–19, 22, 24, 26]. Certain results on weighted generalized inverses are given in [25, 27], while some results regarding the ROL for the group inverse can be found in [2, 10, 20].…”

Section: Introductionmentioning

confidence: 99%

Improvements on the reverse order laws

Cvetković-Ilić

Milenković

2023

Mathematische Nachrichten

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In many papers concerning properties of generalized inverses in different settings, we can find the results with many redundant instances of assuming regularity of certain elements. We have made an effort to widen the range of applicability of concrete results by considering more general cases of the problems without imposing any such additional assumptions. This was the main motivation for this paper, and we present several significant improvements of the reverse order laws on false{1,3false}$\lbrace 1,3\rbrace$ and false{1,2,3false}$\lbrace 1,2,3\rbrace$‐inverses in the ring setting.

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“…Further results on ROL for Moore‐Penrsoe inverse can be found in [13, 15, 21]. The ROL for K ‐inverses, where