The numerical range of banded 2-Toeplitz operators in spaces with an indefinite metric

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.

Keywords:

• indefinite inner product space
• indefinite numerical range
• banded -Toeplitz operator
• tridiagonal operators
• boundary generating curves

AMS Subject Classifications:

• 15A60
• 47B35

Acknowledgments

Thanks are due to the referees for helpful comments.