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The courant-fischer theorem and the spectrum of selfadjoint block band Toeplitz operators |
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| Authors: | Peter Zizler Keith F Taylor Shigeru Arimoto |
| Institution: | (1) Dept. of Math & Stats, Univ. of Saskatchewan, S7N 5E6 Saskatoon, SK, CANADA;(2) Dept. of Math & Stats, Univ. of Saskatchewan, S7N 5E6 Saskatoon, SK, CANADA;(3) Dept. of Chemistry, Univ. of Saskatchewan, S7N 5C9 Saskatoon, SK, CANADA |
| Abstract: | We show that ifT(F) is a selfadjoint block Toeplitz operator generated by a trigonometric matrix polynomialF, then the spectrum ofT(F) as well as the limiting set  (F) of the eigenvalues of the truncationsT
n
(F) is the union of a finite collection of segments (the spectral range ofF) and at most a finite set of points for which we give an upper bound. |
| Keywords: | Primary 47B35 Secondary 15A18 15A47 15A60 42A82 45E10 65F15 |
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