Partial isometries and EP elements in rings with involution

Dijana Mosic, Dragan S. Djordjevic
2009 The Electronic Journal of Linear Algebra  
If R is a ring with involution, and a † is the Moore-Penrose inverse of a ∈ R, then the element a is called: EP, if aa † = a † a; partial isometry, if a * = a † ; star-dagger, if a * a † = a † a * . In this paper, characterizations of partial isometries, EP elements and star-dagger elements in rings with involution are given. Thus, some well-known results are extended to more general settings.
doi:10.13001/1081-3810.1343 fatcat:43jrqjxievhttl4vfd5r7fvfyi