In this article, two results regarding the Moore-Penrose inverse in the frame of C*-algebras are considered. In first place, a characterization of the so-called reverse order law is given, which provides a solution of a problem posed by M. Mbekhta. On the other hand, Moore-Penrose hermitian elements, that is C*-algebra elements which coincide with their Moore-Penrose inverse, are introduced and studied. In fact, these elements will be fully characterized both in the Hilbert space and in the C*-algebra setting. Furthermore, it will be proved that an element is normal and Moore-Penrose hermitian if and only if it is a hermitian partial isometry.
@article{urn:eudml:doc:41853,
title = {On the Moore-Penrose inverse in C*-algebras.},
journal = {Extracta Mathematicae},
volume = {21},
year = {2006},
pages = {93-106},
zbl = {1125.46043},
mrnumber = {MR2292742},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41853}
}
Boasso, Enrico. On the Moore-Penrose inverse in C*-algebras.. Extracta Mathematicae, Tome 21 (2006) pp. 93-106. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41853/