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Characterizations of the polynomial numerical hull of degree k
Authors:James V Burke
Institution:Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, United States
Abstract:Six characterizations of the polynomial numerical hull of degree k are established for bounded linear operators on a Hilbert space. It is shown how these characterizations provide a natural distinction between interior and boundary points. One of the characterizations is used to prove that the polynomial numerical hull of any fixed degree k for a Toeplitz matrix whose symbol is piecewise continuous approaches all or most of that of the infinite-dimensional Toeplitz operator, as the matrix size goes to infinity.
Keywords:15A60  65F15  65F35
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