Resolvent estimates for operators belonging to exponential classes

Details Resolvent estimates for operators belonging to exponential classes Resolvent estimates for operators belonging to exponential classes

2008-09-19

arxiv.org/abs/0809.3385v1

Integr. Equ. Oper. Theory 61 (2008) 21-43

Mathematics

Functional Analysis

AMS-LaTeX, 20 pages

Scientific paper

10.1007/s00020-008-1571-z

For $a,\alpha>0$ let $E(a,\alpha)$ be the set of all compact operators $A$ on a separable Hilbert space such that $s_n(A)=O(\exp(-an^\alpha))$, 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 $E(a,\alpha)$.

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