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Numerical ranges of quadratic operators in spaces with an indefinite metric

Authors: Bebiano, N., Da Providência, J.

Ref.: Electronic Journal of Linear Algebra 26, 141-157 (2013)

Abstract: The numerical range of a quadratic operator acting on an indefinite inner product space is shown to have a hyperbolical shape. This result is extended to different kinds of indefinite numerical ranges, namely, indefinite higher rank numerical ranges and indefinite Davis-Wielandt shells.