# Resolvent estimates for operators belonging to exponential classes - Mathematics > Functional Analysis

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Abstract: For $a,\alpha>0$ let $Ea,\alpha$ be the set of all compact operators $A$ ona separable Hilbert space such that $s nA=O\exp-an^\alpha$, where$s nA$ denotes the $n$-th singular number of $A$. We provide upper bounds forthe norm of the resolvent $zI-A^{-1}$ of $A$ in terms of a quantitydescribing the departure from normality of $A$ and the distance of $z$ to thespectrum of $A$. As a consequence we obtain upper bounds for the Hausdorffdistance of the spectra of two operators in $Ea,\alpha$.

Autor: Oscar F. Bandtlow

Fuente: https://arxiv.org/