# On condition numbers of spectral operators in a hilbert space

On condition numbers of spectral operators in a hilbert space We consider a linear unbounded operator $$A$$ A in a separable Hilbert space. with the following property: there is a normal operator $$D$$ D with a discrete spectrum, such $$\Vert A-D\Vert <\infty$$ ‖ A - D ‖ < ∞ . Besides, all the Eigen values of $$D$$ D are different. Under certain assumptions it is shown that $$A$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

# On condition numbers of spectral operators in a hilbert space

, Volume 5 (4) – Mar 7, 2015
10 pages      /lp/springer-journals/on-condition-numbers-of-spectral-operators-in-a-hilbert-space-ko4lyEI07P
Publisher
Springer Journals
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-015-0100-x
Publisher site
See Article on Publisher Site

### Abstract

We consider a linear unbounded operator $$A$$ A in a separable Hilbert space. with the following property: there is a normal operator $$D$$ D with a discrete spectrum, such $$\Vert A-D\Vert <\infty$$ ‖ A - D ‖ < ∞ . Besides, all the Eigen values of $$D$$ D are different. Under certain assumptions it is shown that $$A$$ 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.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Mar 7, 2015

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