Annals of Functional Analysis

Banach algebra techniques to compute spectra, pseudospectra and condition spectra of some block operators with continuous symbols

G. Krishna Kumar and S. H. Kulkarni

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In this paper we use Banach algebra techniques to study the spectrum, pseudospectrum and condition spectrum of a block Laurent operator with continuous symbol and a lower triangular block Toeplitz operator with continuous symbol.

Article information

Ann. Funct. Anal., Volume 6, Number 1 (2015), 148-169.

First available in Project Euclid: 19 December 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B35
Secondary: 47B48: Operators on Banach algebras 47A10: Spectrum, resolvent 46H35: Topological algebras of operators [See mainly 47Lxx]

spectrum pseudospectrum condition spectrum block operator symbol


Krishna Kumar, G.; Kulkarni, S. H. Banach algebra techniques to compute spectra, pseudospectra and condition spectra of some block operators with continuous symbols. Ann. Funct. Anal. 6 (2015), no. 1, 148--169. doi:10.15352/afa/06-1-12.

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  • Y.A. Abramovich and C.D. Aliprantis, An invitation to operator theory, Graduate Studies in Mathematics, 50, Amer. Math. Soc., Providence, RI, 2002.
  • F.F. Bonsall and J. Duncan, Complete normed algebras, Springer, New York, 1973.
  • A. Böttcher and B. Silbermann, Analysis of Toeplitz operators, second edition, Springer Monographs in Mathematics, Springer, Berlin, 2006.
  • A. Böttcher, Pseudospectra and singular values of large convolution operators, J. Integral Equations Appl. 6 (1994), no. 3, 267–301.
  • I. Feldman, Finiteness of the discrete spectrum of some block Toeplitz operators Integral Equations Operator Theory 16 (1993), no. 3, 385–391.
  • R. Hagen, S. Roch and B. Silbermann, $C\sp *$-algebras and numerical analysis, Monographs and Textbooks in Pure and Applied Mathematics, 236, Dekker, New York, 2001.
  • I. Gohberg, S. Goldberg and M.A. Kaashoek, Basic classes of linear operators, Birkhäuser, Basel, 2003.
  • I. Gohberg, S. Goldberg and M.A. Kaashoek, Classes of linear operators. Vol. II, Operator Theory: Advances and Applications, 63, Birkhäuser, Basel, 1993.
  • I. Gohberg and M.A. Kaashoek, Projection method for block Toeplitz operators with operator-valued symbols Oper. Theory Adv. Appl. 71 (1994), 79–104.
  • G. Krishna Kumar and S.H. Kulkarni, Linear maps preserving pseudospectrum and condition spectrum, Banach J. Math. Anal. 6 (2012), no. 1, (45-60).
  • S.H. Kulkarni and D. Sukumar, The condition spectrum, Acta Sci. Math. (Szeged) 74 (2008), no. 3-4, 625–641.
  • A. Lumsdaine and D. Wu, Spectra and pseudospectra of block Toeplitz matrices, Linear Algebra Appl. 272 (1998), 103–130.
  • L. Reichel and L.N. Trefethen, Eigenvalues and pseudo-eigenvalues of Toeplitz matrices, Linear Algebra Appl. 162/164 (1992), 153–185.
  • S. Roch, P.A. Santos and B. Silbermann, Non-commutative Gelfand theories, Universitext, Springer, London, 2011.
  • A. Rogozhin, The singular value behaviour of finite sections of block Toeplitz operators SIAM J. Matrix Anal. Appl. 27 (2005), no. 1, 273–293.
  • W. Rudin, Functional analysis, Second edition, McGraw-Hill, New York, 1991.
  • L.N. Trefethen and M. Embree, Spectra and pseudospectra, Princeton Univ. Press, Princeton, NJ, 2005.