Numerical ranges of weighted composition operators |
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Authors: | Gajath Gunatillake Mirjana Jovovic Wayne Smith |
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Institution: | 1. Department of Mathematics and Statistics, American University of Sharjah, United Arab Emirates;2. Department of Mathematics, University of Hawaii, Honolulu, HI 96822, United States |
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Abstract: | The operator that takes the function f to ψf°φ is a weighted composition operator. We study numerical ranges of some classes of weighted composition operators on H2, the Hardy–Hilbert space of the unit disc. We consider the case where φ is a rotation of the unit disc and identify a class of convexoid operators. In the case of isometric weighted composition operators we give a complete classification of their numerical ranges. We also consider the inclusion of zero in the interior of the numerical range. |
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Keywords: | Weighted composition operator Numerical range Hardy space |
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