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