Dario Giandinoto: Non self-adjoint block Toeplitz matrices with real asymptotic spectrum

Abstract:

The asymptotic spectrum of Toeplitz and block Toeplitz matrices has been studied extensively, and is described very well by the Theorem of Schmidt-Spitzer. In this talk I will present a condition by Shapiro and Stampach that attempts to characterize Toeplitz matrices with real asymptotic spectrum, by studying the counter-image of the real line through the symbol of the Toeplitz matrices. Then, I will talk about how to generalize this condition in the setting of block Toeplitz matrices, underlining what has been proven and what is left to improve.