Maher, Philip J.; Moslehian, Mohammad Sal More on approximate operators. (English) Zbl 1322.47022 Cubo 14, No. 1, 111-117 (2012). The present note is a continuation of [M. Mirzavaziri, T. Miura and the second author, East J. Approx. 16, No. 2, 147–151 (2010; Zbl 1321.47033)]. The main result of the paper is the following.Theorem. If \(T\) is an invertible contraction in \(\mathcal L (H)\) and \(\| TT^*T-T\| <\varepsilon<\frac{2}{3\sqrt 3}\), then there exists a partial isometry \(V\) such that \(\| T-V\| <K\varepsilon\) for a certain constant \(K>0\). Reviewer: Dorel Miheţ (Timişoara) Cited in 1 Document MSC: 47A55 Perturbation theory of linear operators 39B52 Functional equations for functions with more general domains and/or ranges Keywords:partial isometry; approximate generalized inverse, invertible contraction Citations:Zbl 1321.47033 PDFBibTeX XMLCite \textit{P. J. Maher} and \textit{M. S. Moslehian}, Cubo 14, No. 1, 111--117 (2012; Zbl 1322.47022) Full Text: DOI