Generalized inverses in C*-algebras, 2

Maher, Philip (2007) Generalized inverses in C*-algebras, 2. Rendiconti del Circolo Matematico di Palermo, 56 (2). pp. 459-463. ISSN 0009-725X

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Official URL: http://dx.doi.org/10.1007/BF03032096

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Abstract

We first complete, and second extend, the work begun in the paper "Generalized inverses in C*-algebras". The paper, which recaptured the elementary theory of generalized inversesin the context of C*-algebras, contained an omission: it left open whether or not generalized inverses actually exist. Here, first, we give a condition (Theorem 4) for the existence of a generalized inverse of an element of a C*-algebra. Second, the paper contained a "right-handed" inequality to do with minimizing ||ax-c|| (and a corresponding "left-handed" one to do with minimizing ||xb-c||). Here, we obtain a "double-sided" result on minimizing ||axb-c|| (which subsumes the results of the paper on minimizing ||ax-c|| and ||xb-c||).

Item Type:Article
Research Areas:School of Science and Technology > Design Engineering and Mathematics
ID Code:9219
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Deposited On:26 Jun 2012 09:58
Last Modified:13 May 2014 15:47

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