Characterizations of the polynomial numerical hull of degree k |
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Authors: | James V Burke |
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Institution: | Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, United States |
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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. |
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Keywords: | 15A60 65F15 65F35 |
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