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 discrete spectrum such that $\|(A-S)S^{-\nu}\|<\infty$ for a $\nu\in [0,1]$. Besides, all eigenvalues of $S$ are assumed to be 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.
Key words: Similarity, differential operator, spectrum perturbations, operator function.
Full Text
Article Information
| Title | On similarity of unbounded perturbations of selfadjoint operators |
| Source | Methods Funct. Anal. Topology, Vol. 24 (2018), no. 1, 27-33 |
| MathSciNet |
MR3783815 |
| Milestones | Received 13/04/2017; Revised 05/10/2017 |
| Copyright | The Author(s) 2018 (CC BY-SA) |
Authors Information
Michael Gil'
Department of Mathematics, Ben Gurion University of the Negev, P.0. Box 653, BeerSheva 84105, Israel
Citation Example
Michael Gil', On similarity of unbounded perturbations of selfadjoint operators, Methods Funct. Anal. Topology 24
(2018), no. 1, 27-33.
BibTex
@article {MFAT1022,
AUTHOR = {Michael Gil'},
TITLE = {On similarity of unbounded perturbations of selfadjoint operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {24},
YEAR = {2018},
NUMBER = {1},
PAGES = {27-33},
ISSN = {1029-3531},
MRNUMBER = {MR3783815},
URL = {http://mfat.imath.kiev.ua/article/?id=1022},
}
