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Title: Biorthogonality and generalised k-numerical ranges
Author: Felton, A. J.
Awarding Body: University College of Swansea
Current Institution: Swansea University
Date of Award: 1995
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This thesis is presented in two parts followed by a brief Appendix. The two parts are independent, and each has its own bibliography. In Part I we introduce a concept of 'biorthogonality' in a smooth normed linear space. In Part II we look at generalisations of Halmos' k-numerical range and associated k-numerical radius for an operator on a Hilbert space. These generalisations again apply to Hilbert-space-operators. We study the rate of growth, as k tend to infinity, of these generalised k-numerical radii of von Neumann-Schatten class operators. In particular, for one such generalisation, we characterise trace-class operators in terms of this rate of growth. In the Appendix, we suggest a natural extension of Halmos' concept of k-numerical range to that for an operator on a general smooth normed linear space. Elementary properties are given, but a deeper development of the theory of such a k-numerical range is left as an open problem.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available