Finite sections of truncated Toeplitz operators

Steffen Roch 1
  • 1 Technische Universität Darmstadt, Fachbereich Mathematik, Schlossgartenstrasse 7, 64289 Darmstadt, Germany


We describe the C*-algebra associated with the finite sections discretization of truncated Toeplitz operators on the model space K2u where u is an infinite Blaschke product. As consequences, we get a stability criterion for the finite sections discretization and results on spectral and pseudospectral approximation.

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  • [1] Roch, S., Silbermann, B., C*-algebra techniques in numerical analysis, J. Oper. Theory, 1996, 2, 241-280

  • [2] Roch, S., Silbermann, B., Index calculus for approximation methods and singular value decomposition, J.Math. Anal. Appl., 1998, 401-426

  • [3] Sarason, D., Algebraic properties of truncated Toeplitz operators, Oper. Matrices, 2007, 4, 491-526

  • [4] Treil, S.R., Invertibility of Toeplitz operators does not imply applicability of the finite section method, Dokl. Akad. Nauk SSSR, 1987, 3, 563-567 (Russian)

  • [5] Böttcher, A., Silbermann, B., Introduction to Large Truncated Toeplitz Matrices, Springer-Verlag, Berlin, Heidelberg, 1999

  • [6] Hagen, R., Roch, S., Silbermann, B., C*-Algebras and Numerical Analysis, Marcel Dekker, Inc., New York, Basel, 2001

  • [7] Nikolski, N.K., Treatise on the Shift Operator, Springer-Verlag, Berlin, 1986

  • [8] Garcia, S.R., Ross, W.T., Wogen, W.R., C*-algebras generated by truncated Toeplitz operators, In: Cepedello Boiso, M., Hedenmalm, H., Kaashoek, M., Montes Rodriguez, A., Treil, S. (Eds). Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation, 22nd Workshop in Operator Theory and Its Applications (Sevilla, July 2011), Springer, Basel, 2014, 181-192


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