On the Moore-Penrose inverse in C*-algebras

Autores: Enrico Boasso
Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 21, Nº 2, 2006, págs. 93-106
Idioma: inglés
Títulos paralelos:
- Sobre el inverso Moore-Penrose en C*-álgebras
Enlaces
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Resumen
- 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.