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More on approximate operators. (English) Zbl 1322.47022

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 \(K>0\).

MSC:

47A55 Perturbation theory of linear operators
39B52 Functional equations for functions with more general domains and/or ranges

Citations:

Zbl 1321.47033
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