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On Generalized Numerical Ranges of Quadratic Operators

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Recent Advances in Matrix and Operator Theory

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 179))

Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, College of William and Mary Williamsburg, VA, 23185, USA

    Leiba Rodman & Ilya M. Spitkovsky

Authors
  1. Leiba Rodman
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  2. Ilya M. Spitkovsky
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA

    Joseph A. Ball

  2. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    Yuli Eidelman

  3. Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, California, 92093-0112, USA

    J. William Helton

  4. Department of Mathematics, University of Connecticut, 196 Auditorium Road, U-9, Storrs, CT, 06269, USA

    Vadim Olshevsky

  5. Department of Mathematics, University of Virginia, P. O. Box 400137, Charlottesville, VA, 22904-4137, USA

    James Rovnyak

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Rodman, L., Spitkovsky, I.M. (2007). On Generalized Numerical Ranges of Quadratic Operators. In: Ball, J.A., Eidelman, Y., Helton, J.W., Olshevsky, V., Rovnyak, J. (eds) Recent Advances in Matrix and Operator Theory. Operator Theory: Advances and Applications, vol 179. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8539-2_15

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