Normal approximants for certain toeplitz matrices and toeplitz operators
Date
1995
Authors
Harrison, Robert Norman
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Abstract
In 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.