Abstract
The numerical range of banded -Toeplitz operators acting on a Hilbert space endowed with an indefinite metric is investigated. The indefinite numerical range is completely characterized by performing a reduction to the two-dimensional underlying space. The parametric equations of the boundary generating curves are provided. Particular attention is paid to the case of tridiagonal
-Toeplitz operators. Classes of these operators with an indefinite hyperbolical range are identified. Our main focus is on infinite dimensional spaces.
Acknowledgments
Thanks are due to the referees for helpful comments.