Resolvent Estimates for Operators Belonging to Exponential Classes |
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Authors: | Oscar F Bandtlow |
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Institution: | (1) School of Mathematical Sciences, Queen Mary, University of London, London, E3 4NS, UK |
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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(-anα)), 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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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 47A10 Secondary 47B06 47B07 |
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