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Lindner, Marko ; Silbermann, Bernd : Finite Sections in an Algebra of Convolution and Multiplication Operators on $L^\infty(R)$

Lindner, Marko ; Silbermann, Bernd : Finite Sections in an Algebra of Convolution and Multiplication Operators on $L^\infty(R)$

Author(s):
Lindner, Marko
Silbermann, Bernd
Title:
Finite Sections in an Algebra of Convolution and Multiplication Operators on $L^\infty(R)$
Electronic source:
application/postscript
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 6, 2000
Mathematics Subject Classification:
47B38 [ Operators on function spaces ]
65J10 [ Equations with linear operators ]
Abstract:
This text is concerned with the applicability of the finite section method to a certain type of operators on $L^\infty(R)$. These operators belong to the smallest closed algebra generated by convolution operators with symbol in the Wiener algebra and operators of multiplication by bounded functions with limits at plus and minus infinity. We use Banach algebra techniques to show that the finite section method is applicable to some operator $A$ in that algebra if and only if $A$ and an associated operator $\tilde A$ are invertible.
Keywords:

Language:
English
Publication time:
3 / 2002