Abstract
We consider a linear unbounded operator \(A\) in a separable Hilbert space. with the following property: there is a normal operator \(D\) with a discrete spectrum, such \(\Vert A-D\Vert <\infty \). Besides, all the Eigen values of \(D\) are different. Under certain assumptions it is shown that \(A\) is similar to a normal operator and a sharp bound for the condition number is suggested. Applications of that bound to spectrum perturbations and operator functions are also discussed. As an illustrative example we consider a non-selfadjoint differential operator.
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Gil’, M. On condition numbers of spectral operators in a hilbert space. Anal.Math.Phys. 5, 363–372 (2015). https://doi.org/10.1007/s13324-015-0100-x
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DOI: https://doi.org/10.1007/s13324-015-0100-x