The numerical range of a periodic tridiagonal operator reduces to the numerical range of a finite matrix

Abstract

In this paper we show that the closure of the numerical range of an $n+1$-periodic tridiagonal operator is equal to the numerical range of a $2(n+1)\times 2(n+1)$ complex matrix.

arXiv comment14 pages

References in corpus (7)

• Determinantal representations of hyperbolic plane curves: An elementary approach
• Spectral Curves of Non-Hermitean Hamiltonians
• Computing Linear Matrix Representations of Helton-Vinnikov Curves
• The Eigenvalues of Tridiagonal Sign Matrices are Dense in the Spectra of Periodic Tridiagonal Sign Operators
• Eigenvalue problem meets Sierpinski triangle: computing the spectrum of a non-self-adjoint random operator
• A class of tridiagonal operators associated to some subshifts
• The numerical range of a class of periodic tridiagonal operators

Cited by in corpus (1)

• The numerical range of periodic banded Toeplitz operators