The numerical range of a class of periodic tridiagonal operators

Abstract

In this paper we compute the closure of the numerical range of certain periodic tridiagonal operators. This is achieved by showing that the closure of the numerical range of such operators can be expressed as the closure of the convex hull of the uncountable union of numerical ranges of certain symbol matrices. For a special case, this result can be improved so that it is the convex hull of the union of the numerical ranges of only two matrices. A conjecture is stated for the general case.

arXiv comment22 pages, 3 figures

References in corpus (4)

• Spectral Curves of Non-Hermitean Hamiltonians
• 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

Cited by in corpus (3)

• The numerical range of a periodic tridiagonal operator reduces to the numerical range of a finite matrix
• The numerical range of some periodic tridiagonal operators is the convex hull of the numerical ranges of two finite matrices
• The numerical range of periodic banded Toeplitz operators