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    Quantitative Perturbation Theory for Compact Operators on a Hilbert Space 
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    Quantitative Perturbation Theory for Compact Operators on a Hilbert Space

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    GUVEN_Ayse_PhD_Final_170816.pdf (581.4Kb)
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    Queen Mary University of London
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    Abstract
    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.
    Authors
    Guven, Ayse
    URI
    http://qmro.qmul.ac.uk/xmlui/handle/123456789/23197
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    • Theses [3593]
    Licence information
    The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without the prior written consent of the author
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