THE COURANT-FISCHER THEOREM AND THE SPECTRUM OF SELF-ADJOINT BLOCK BAND TOEPLITZ-OPERATORS

Citation
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
Citations number
8
Categorie Soggetti
Mathematics, Pure",Mathematics,Mathematics
ISSN journal
0378620X
Volume
28
Issue
2
Year of publication
1997
Pages
245 - 250
Database
ISI
SICI code
0378-620X(1997)28:2<245:TCTATS>2.0.ZU;2-C
Abstract
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.