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Integral Equations and Operator Theory

, Volume 28, Issue 2, pp 245–250 | Cite as

The courant-fischer theorem and the spectrum of selfadjoint block band Toeplitz operators

  • Peter Zizler
  • Keith F. Taylor
  • Shigeru Arimoto
Short Communications

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 Λ(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.

MSC 1991

Primary 47B35 Secondary 15A18 15A47 15A60 42A82 45E10 65F15 

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Copyright information

© Birkhäuser Verlag 1997

Authors and Affiliations

  • Peter Zizler
    • 1
  • Keith F. Taylor
    • 2
  • Shigeru Arimoto
    • 3
  1. 1.Dept. of Math & StatsUniv. of SaskatchewanSaskatoonCANADA
  2. 2.Dept. of Math & StatsUniv. of SaskatchewanSaskatoonCANADA
  3. 3.Dept. of ChemistryUniv. of SaskatchewanSaskatoonCANADA

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