P. Zizler et al., THE COURANT-FISCHER THEOREM AND THE SPECTRUM OF SELF-ADJOINT BLOCK BAND TOEPLITZ-OPERATORS, Integral equations and operator theory, 28(2), 1997, pp. 245-250
We show that if T(F) is a selfadjoint block Toeplitz operator generate
d by a trigonometric matrix polynomial F, then the spectrum of T(F) as
well as the limiting set Lambda(F) of the eigenvalues of the truncati
ons T-n(F) is the union of a finite collection of segments (the spectr
al range of F) and at most a finite set of points for which we give an
upper bound.