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The finite section method in the space of essentially bounded functions: An approach using limit operators
Publikationstyp
Journal Article
Date Issued
2003-02-07
Sprache
English
Author(s)
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.
Subjects
Band-dominated operators
Finite section method
Invertibility at infinity
Limit operators
Stability
DDC Class
510: Mathematik