Generalized inverses in \(C^*\)-algebras. II (Q2467959)

This paper is a continuation of [\textit{P.\,J.\thinspace Maher}, Rend.\ Circ.\ Mat.\ Palermo (2) 55, No.\,3, 441--448 (2006; Zbl 1146.47026), see the preceding review]. Using the Gelfand--Naimark theorem to lift the results on bounded linear operators acting on a Hilbert space to the context of \(C^*\)-algebras, the author shows that an element \(a\) in a \(C^*\)-algebra \(A\) has a unique Moore--Penrose inverse if there is a projection \(p\in A\) such that \(pa=a\). He also gives some results on minimizing \(\|axb-c\|\,(x\in A)\).