On Generalized Numerical Ranges of Quadratic Operators

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It is shown that the result of Tso-Wu on the elliptical shape of the numerical range of quadratic operators holds also for the essential numerical range. The latter is described quantitatively, and based on that sufficient conditions are established under which the c-numerical range also is an ellipse. Several examples are considered, including singular integral operators with the Cauchy kernel and composition operators.
14 pages

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Functional Analysis, 47A12; 45E05, 47B33, 47B35

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http://salesiana.dossiersoluciones.com/handle/123456789/108971

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0602318
 http://arxiv.org/abs/math/0602318

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arXiv