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arXiv · 0809.3385

Resolvent estimates for operators belonging to exponential classes

Oscar F. Bandtlow
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Abstract

For $a,α>0$ let $E(a,α)$ be the set of all compact operators $A$ on a separable Hilbert space such that $s_n(A)=O(\exp(-an^α))$, where $s_n(A)$ denotes the $n$-th singular number of $A$. We provide upper bounds for the norm of the resolvent $(zI-A)^{-1}$ of $A$ in terms of a quantity describing the departure from normality of $A$ and the distance of $z$ to the spectrum of $A$. As a consequence we obtain upper bounds for the Hausdorff distance of the spectra of two operators in $E(a,α)$.

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Oscar F. Bandtlow. 2008-09-19. Resolvent estimates for operators belonging to exponential classes. https://doi.org/10.1007/s00020-008-1571-z

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