Range projections and the Moore-Penrose inverse in rings with involution

• Published in: Linear & multilinear algebra Vol. 55; no. 2; pp. 103 - 112
• Main Authors: Koliha, J. J., RakoČević, V.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 01.03.2007
• Subjects: 2000 Mathematics Subject Classifications: 46L05; C-algebra; Idempotent; Moore-Penrose inverse; Range projection

In this article we study the existence of range projections in rings with involution, relating it to the existence of the Moore-Penrose inverse. The results are applied to the solution of the equation xbx = x in rings with involution, extending the results of Greville for matrices. Simpler new proof...