Frantisek Stampach: Non-self-adjoint Toeplitz matrices with purely real spectrum.

Abstract: We show a sufficient condition on the symbol of a (possibly non-self-adjoint) Toeplitz matrix guaranteeing the spectrum of its principal submatrix of an arbitrary size is purely real. In case of banded Toeplitz matrices, we provide a complete characterization of the class of matrices with the above property. Next, we describe how the eigenvalues of the principal submatrices distribute on the real line as the size goes to infinity. The presented results will be demonstrated by concrete examples.