Lindner, Marko : Fredholmness and index of operators in the Wiener algebra are independent of the underlying space.
- Fredholmness and index of operators in the Wiener algebra are independent of the underlying space.
- Electronic source:
- 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 ]
- 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.
- Fredholm operator, Fredholm index, Wiener algebra, operators on $\ell^p$ spaces.
- Publication time:
- 2 / 2008