Abstract and Applied Analysis
Volume 2014, Article ID 309708, 6 pages
http://dx.doi.org/10.1155/2014/309708
On the Covariance of Moore-Penrose Inverses in Rings with Involution
Department of Mathematics, Islamic Azad University, Firoozkooh Branch, Firoozkooh, Iran
Received 17 February 2014; Revised 14 April 2014; Accepted 14 April 2014; Published 5 May 2014
Academic Editor: Sergei V. Pereverzyev
Copyright © 2014 Hesam Mahzoon. 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.
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 is a regular element in a -algebra, then the covariance set of is closed in the set of invertible elements (with relative topology) of -algebra and is a cone in the -algebra.