Abstract
We consider a linear unbounded operator A in a separable Hilbert space with the following property: there is an invertible selfadjoint operator S with a dis- crete spectrum such that ∥(A-S)S-v∥ <∞ for a v ε [0, 1]. Besides, all eigenvalues of S are assumed to be different. Under certain assumptions it is shown that A is si- milar 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.
Original language | English |
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Pages (from-to) | 27-33 |
Number of pages | 7 |
Journal | Methods of Functional Analysis and Topology |
Volume | 24 |
Issue number | 1 |
State | Published - 1 Jan 2018 |
Keywords
- Operator function
- Similarity
- Spectrum perturbations
- differential operator
ASJC Scopus subject areas
- Analysis
- Mathematical Physics
- Geometry and Topology