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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 918107, 5 pages
http://dx.doi.org/10.1155/2014/918107
Research Article

Weighted Dual Covariance Moore-Penrose Inverses with respect to an Invertible Element in -Algebras

Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran

Received 31 May 2014; Accepted 6 July 2014; Published 16 July 2014

Academic Editor: Ferenc Hartung

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 study several algebraic properties of dual covariance and weighted dual covariance sets in rings with involution and -algebras. Moreover, we show that the weighted dual covariance set, seen as a multivalued map, has some kind of continuity. Also, we prove weighed dual covariance set invariant under the bijection multiplicative -functions.