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Title: Quantitative perturbation theory for compact operators on a Hilbert space
Author: Guven, Ayse
ISNI:       0000 0004 7652 023X
Awarding Body: Queen Mary University of London
Current Institution: Queen Mary, University of London
Date of Award: 2016
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This thesis makes novel contributions to a problem of practical and theoretical importance, namely how to determine explicitly computable upper bounds for the Hausdorff distance of the spectra of two compact operators on a Hilbert space in terms of the distance of the two operators in operator norm. It turns out that the answer depends crucially on the speed of decay of the sequence of singular values of the two operators. To this end, 'compactness classes', that is, collections of operators the singular values of which decay at a certain speed, are introduced and their functional analytic properties studied in some detail. The main result of the thesis is an explicit formula for the Hausdorff distance of the spectra of two operators belonging to the same compactness class. Along the way, upper bounds for the resolvents of operators belonging to a particular compactness class are established, as well as novel bounds for determinants of trace class operators.
Supervisor: Not available Sponsor: Turkish Ministry of National Education
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Hausdorff distance ; Hilbert space ; operator norm