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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Bibliographic Details
Published inAbstract and Applied Analysis Vol. 2014; no. 2014; pp. 39 - 44-405
Main Author Mahzoon, Hesam
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2014
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Hindawi Limited
Wiley
Subjects
Algebra
Functions, Inverse
Mathematical research
Rings (Algebra)
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Summary: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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/309708