Normal approximants for certain toeplitz matrices and toeplitz operators

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dc.contributor.authorHarrison, Robert Normanen_US
dc.date.accessioned2024-08-14T16:44:22Z
dc.date.available2024-08-14T16:44:22Z
dc.date.copyright1995en_US
dc.date.issued1995
dc.degree.departmentDepartment of Mathematics and Statistics
dc.degree.levelMaster of Science M.Sc.en
dc.description.abstractIn this thesis, we consider the normal approximation problem for certain Toeplitz matrices and Toeplitz operators, with respect to the operator norm. For upper triangular Toeplitz matrices, we exh1b1t a natural normal approximant, and show that it is a best normal approximant in certain fundamental cases. In other cases, we analyze its effectiveness as a distance estimate by comparing it to the standard Hermitian approximant. For Toeplitz operators induced by certain continuous functions on the unit circle, we obtain upper and lower bounds on the distance to the set of normal operators, in terms of the image of the unit circle. In particular, if the continuous function is one-to-one and the image is a circle, then the distance to the normals is the radius of the image circle.
dc.format.extent102 pages
dc.identifier.urihttps://hdl.handle.net/1828/18057
dc.rightsAvailable to the World Wide Weben_US
dc.titleNormal approximants for certain toeplitz matrices and toeplitz operatorsen_US
dc.typeThesisen_US

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