On the Covariance of Moore-Penrose Inverses in Rings with Involution
We consider the so-called covariance set of Moore-Penrose inverses in rings with an involution. We deduce some new results concerning covariance set. We will show that if a is a regular element in a C ∗ -algebra, then the covariance set of a is closed in the set of invertible elements (with relative...
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| Published in | Abstract and Applied Analysis Vol. 2014; no. 2014; pp. 39 - 44-405 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cairo, Egypt
Hindawi Limiteds
01.01.2014
Hindawi Publishing Corporation John Wiley & Sons, Inc Hindawi Limited Wiley |
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| Online Access | Get full text |
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| Abstract | We consider the so-called covariance set of Moore-Penrose inverses in rings with an involution. We deduce some new results concerning covariance set. We will show that if a is a regular element in a C ∗ -algebra, then the covariance set of a is closed in the set of invertible elements (with relative topology) of C ∗ -algebra and is a cone in the C ∗ -algebra. |
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| AbstractList | We consider the so-called covariance set of Moore-Penrose inverses in rings with an involution. We deduce some new results concerning covariance set. We will show that if a is a regular element in a {C}^{\ast } -algebra, then the covariance set of a is closed in the set of invertible elements (with relative topology) of {C}^{\ast } -algebra and is a cone in the {C}^{\ast } -algebra. We consider the so-called covariance set of Moore-Penrose inverses in rings with an involution. We deduce some new results concerning covariance set. We will show that if a is a regular element in a C ∗ -algebra, then the covariance set of a is closed in the set of invertible elements (with relative topology) of C ∗ -algebra and is a cone in the C ∗ -algebra. We consider the so-called covariance set of Moore-Penrose inverses in rings with an involution. We deduce some new results concerning covariance set. We will show that if a is a regular element in a C ∗ -algebra, then the covariance set of a is closed in the set of invertible elements (with relative topology) of C ∗ -algebra and is a cone in the C ∗ -algebra. We consider the so-called covariance set of Moore-Penrose inverses in rings with an involution. We deduce some new results concerning covariance set. We will show that if a is a regular element in a C∗-algebra, then the covariance set of a is closed in the set of invertible elements (with relative topology) of C∗-algebra and is a cone in the C∗-algebra. We consider the so-called covariance set of Moore-Penrose inverses in rings with an involution. We deduce some new results concerning covariance set. We will show that if a is a regular element in a [C.sup.*]- algebra, then the covariance set of a is closed in the set of invertible elements (with relative topology) of [C.sup.*]-algebra and is a cone in the [C.sup.*]-algebra. We consider the so-called covariance set of Moore-Penrose inverses in rings with an involution. We deduce some new results concerning covariance set. We will show that if a is a regular element in a [superscript] C [low *] [/superscript] -algebra, then the covariance set of a is closed in the set of invertible elements (with relative topology) of [superscript] C [low *] [/superscript] -algebra and is a cone in the [superscript] C [low *] [/superscript] -algebra. |
| Audience | Academic |
| Author | Mahzoon, Hesam |
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| Cites_doi | 10.1016/0024-3795(83)80040-8 10.4064/sm-103-1-71-77 10.1080/03081080802652279 10.1016/0024-3795(84)90024-7 10.7146/math.scand.a-14320 |
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| Copyright | Copyright © 2014 Hesam Mahzoon. COPYRIGHT 2014 John Wiley & Sons, Inc. Copyright © 2014 Hesam Mahzoon. Hesam Mahzoon et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Copyright 2014 Hindawi Publishing Corporation |
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| References | (3) 1992; 18 (6) 2002; 10 (4) 1983; 52-53 (5) 1992; 103 (2) 1984; 61 (1) 2010; 58 (7) 2001; 88 3 (8) 1992; 103 (2) 1992; 18 5 (6) 2001; 88 7 (1) 2002; 10 |
| References_xml | – volume: 103 start-page: 71 issue: 1 year: 1992 end-page: 77 ident: 5 article-title: On generalized inverses in -algebras publication-title: – volume: 88 start-page: 154 issue: 1 year: 2001 end-page: 160 ident: 7 article-title: Continuity and differentiability of the Moore-Penrose inverse in -algebras publication-title: – volume: 10 start-page: 141 issue: 2 year: 2002 end-page: 148 ident: 6 article-title: Generalized inverses of products publication-title: – volume: 61 start-page: 91 year: 1984 end-page: 99 ident: 2 article-title: On the covariance of the Moore-Penrose inverse publication-title: – volume: 18 start-page: 167 issue: 2 year: 1992 end-page: 174 ident: 3 article-title: Some remarks on the covariance of the Moore-Penrose inverse publication-title: – volume: 52-53 start-page: 629 year: 1983 end-page: 643 ident: 4 article-title: On the covariance of the Moore-Penrose inverse publication-title: – volume: 58 start-page: 445 issue: 3-4 year: 2010 end-page: 452 ident: 1 article-title: Moore-Penrose invertibility in involutory rings: the case publication-title: – ident: 5 doi: 10.1016/0024-3795(83)80040-8 – volume: 10 start-page: 141 issue: 2 year: 2002 ident: 1 publication-title: International Journal of Applied Mathematics – volume: 18 start-page: 167 issue: 2 year: 1992 ident: 2 publication-title: Houston Journal of Mathematics – volume: 103 start-page: 71 issue: 1 year: 1992 ident: 8 publication-title: Studia Mathematica doi: 10.4064/sm-103-1-71-77 – ident: 7 doi: 10.1080/03081080802652279 – ident: 3 doi: 10.1016/0024-3795(84)90024-7 – volume: 88 start-page: 154 issue: 1 year: 2001 ident: 6 publication-title: Mathematica Scandinavica doi: 10.7146/math.scand.a-14320 |
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| Snippet | We consider the so-called covariance set of Moore-Penrose inverses in rings with an involution. We deduce some new results concerning covariance set. We will... |
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| Title | On the Covariance of Moore-Penrose Inverses in Rings with Involution |
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