abs_vol22_pp92-111. 23KB Jun 04 2011 12:05:49 AM

ELA

REVERSE ORDER LAW FOR THE MOORE-PENROSE

INVERSE IN

C

∗

-ALGEBRAS

∗

DIJANA MOSI ´C† _{AND DRAGAN S. DJORDJEVI ´C}†

Abstract. In this paper, several equivalent conditions related to the reverse order law for

the Moore-Penrose inverse in C∗_{-algebras are studied. Some well-known results are extended to}

more general settings. Then this result is applied to obtain the reverse order rule for the weighted

Moore-Penrose inverse inC∗_-algebras.

Key words. Moore-Penrose inverse, Reverse order law,C∗_-algebras.

AMS subject classifications. 16W10, 15A09, 46L05.

∗_{Received by the editors on July 24, 2010. Accepted for publication on January 31, 2011. Handling}

Editor: Michael Tsatsomeros.

†_{Faculty of Sciences and Mathematics, University of Niˇs, P.O. Box 224, 18000 Niˇs, Serbia}

(di-jana@pmf.ni.ac.rs, dragan@pmf.ni.ac.rs). The authors were supported by the Ministry of Science, Republic of Serbia, grant no. 174007.

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 22, pp. 92-111, February 2011