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On Generalized Numerical Ranges of Quadratic Operators

Functional Analysis 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.math/0602318,
  title  = {On Generalized Numerical Ranges of Quadratic Operators},
  author = {Leiba Rodman and Ilya M. Spitkovsky},
  journal= {arXiv preprint arXiv:math/0602318},
  year   = {2007}
}

Comments

14 pages

R2 v1 2026-07-22T17:31:32.972Z