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# The finite section method in the space of essentially bounded functions: An approach using limit operators

Publikationstyp

Journal Article

Publikationsdatum

2003-02-07

Sprache

English

Author

Enthalten in

Volume

24

Issue

7-8

Start Page

863

End Page

893

Citation

Numerical Functional Analysis and Optimization 24 (7-8): 863-893 (2003-01-01)

Publisher DOI

Scopus ID

We present an approach to the finite section method for band-dominated operators - the norm-limits of band operators on L∞(ℝn). We hereby show that the sequence of finite sections is stable if and only if some associated operator is invertible at infinity. By means of the theory in Lindner and Silbermann (Lindner, M., Silbermann, B. (2003). Invertibility at infinity of band-dominated operators in the space of essentially bounded functions, (accepted at) Integral Equations and Operator Theory.) and Lindner (Lindner, M. (2003). Classes of multiplication operators and their limit operators (submitted to) Zeitschrift für Analysis und ihre Anwendungen), we study this invertibility at infinity using limit operators. Having the mentioned criterion at our disposal, we will give some applications in an algebra of convolution and multiplication operators: one for the usual finite section method and one for an approximation method of operators on the space of continuous functions.