# Finite sections of truncated Toeplitz operators

Concrete Operators (2015)

- Volume: 2, Issue: 1, page 8-16, electronic only
- ISSN: 2299-3282

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topSteffen Roch. "Finite sections of truncated Toeplitz operators." Concrete Operators 2.1 (2015): 8-16, electronic only. <http://eudml.org/doc/268900>.

@article{SteffenRoch2015,

abstract = {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.},

author = {Steffen Roch},

journal = {Concrete Operators},

keywords = {Model spaces; truncated Toeplitz operators; Widom’s identity; stability of the finite sections discretization; model spaces; Widom's identity},

language = {eng},

number = {1},

pages = {8-16, electronic only},

title = {Finite sections of truncated Toeplitz operators},

url = {http://eudml.org/doc/268900},

volume = {2},

year = {2015},

}

TY - JOUR

AU - Steffen Roch

TI - Finite sections of truncated Toeplitz operators

JO - Concrete Operators

PY - 2015

VL - 2

IS - 1

SP - 8

EP - 16, electronic only

AB - 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.

LA - eng

KW - Model spaces; truncated Toeplitz operators; Widom’s identity; stability of the finite sections discretization; model spaces; Widom's identity

UR - http://eudml.org/doc/268900

ER -

## References

top- [1] Roch, S., Silbermann, B., C*-algebra techniques in numerical analysis, J. Oper. Theory, 1996, 2, 241-280 Zbl0865.65035
- [2] Roch, S., Silbermann, B., Index calculus for approximation methods and singular value decomposition, J.Math. Anal. Appl., 1998, 401-426 Zbl0923.65026
- [3] Sarason, D., Algebraic properties of truncated Toeplitz operators, Oper. Matrices, 2007, 4, 491-526 Zbl1144.47026
- [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 Zbl0916.15012
- [6] Hagen, R., Roch, S., Silbermann, B., C*-Algebras and Numerical Analysis, Marcel Dekker, Inc., New York, Basel, 2001 Zbl0964.65055
- [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 Zbl1323.47082

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