Generalized inverses in C*-algebras
Maher, Philip (2006) Generalized inverses in C*-algebras. Rendiconti del Circolo Matematico di Palermo, 55 (2). pp. 441-448. ISSN 0009-725X
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Official URL: http://dx.doi.org/10.1007/BF02874781
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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 , . 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.
|Research Areas:||Science & Technology > Mathematics & Statistics|
|Deposited On:||24 Oct 2008 12:25|
|Last Modified:||06 Feb 2013 11:22|
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