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

Authors: Bebiano, N., da ProvidĂȘncia, J., Nata, A.

Ref.: Linear and Multilinear Algebra Article in Press (2013)

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