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Fakultät für Mathematik
Lindner, Marko : Fredholmness and index of operators in the Wiener algebra are independent of the underlying space.

Lindner, Marko : Fredholmness and index of operators in the Wiener algebra are independent of the underlying space.


Author(s):
Lindner, Marko
Title:
Fredholmness and index of operators in the Wiener algebra are independent of the underlying space.
Electronic source:
application/pdf
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 1, 2008
Mathematics Subject Classification:
47A53 [ Fredholm operators; index theories ]
46E40 [ Spaces of vector- and operator-valued functions ]
47B37 [ Operators on special spaces ]
47L10 [ Algebras of operators on Banach spaces and other topological linear spaces ]
Abstract:
The purpose of this paper is to demonstrate the so-called Fredholm-inverse closedness of the Wiener algebra $W$ and to deduce independence of the Fredholm property and index of the underlying space. More precisely, we look at operators $A\in W$ as acting on a family of vector valued $\ell^p$ spaces and show that the Fredholm regularizer of $A$ for one of these spaces can always be chosen in $\W$ as well and therefore regularizes $A$ (modulo compact operators) on all of the $\ell^p$ spaces under consideration. We conclude that both Fredholmness and the index of $A$ do not depend on the $\ell^p$ space that $A$ is considered as acting on.
Keywords:
Fredholm operator, Fredholm index, Wiener algebra, operators on $\ell^p$ spaces.
Language:
English
Publication time:
2 / 2008

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