Generalized inverses in C*-algebras


Maher, P. 2006. Generalized inverses in C*-algebras. Rendiconti del Circolo Matematico di Palermo. 55 (2), pp. 441-448.
TitleGeneralized inverses in C*-algebras
AuthorsMaher, P.

In this paper we present the elementary theory of generalized inverses in the context of C*-algebras. We recapture and, where necessary, modify some of the well-known results of [6], [7]. The methods are, of course, algebraic rather than geometric: there can be no references to ranges or kernels. For this reason we are unable to demonstrate the existence of the Moore-Penrose inverse (and hence the existence of generalized inverses): although we are able to give a criterion, (Theorem 3), a variant of Penrose's [6, Theorem 1] for there to be no. more than one generalized inverse. Other results are recaptured in this setting.

JournalRendiconti del Circolo Matematico di Palermo
Publication dates
Print30 Jan 2006
Publication process dates
Deposited24 Oct 2008
Output statusPublished
Digital Object Identifier (DOI)
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