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Fredholmness and index of operators in the Wiener algebra are independent of the underlying space
Publikationstyp
Journal Article
Date Issued
2008
Sprache
English
Author(s)
Journal
Issue
2
Start Page
297
End Page
306
Citation
Operators and Matrices (2): 297-306 (2008)
Publisher DOI
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 ∈ W as acting on a family of
vector valued 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 p spaces under consideration. We conclude that both Fredholmness and the index of
A do not depend on the p space that A is considered as acting on.
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 ∈ W as acting on a family of
vector valued 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 p spaces under consideration. We conclude that both Fredholmness and the index of
A do not depend on the p space that A is considered as acting on.
Subjects
Fredholm operator
Fredholm index
Wiener algebra
operators on ℓp spaces
DDC Class
510: Mathematik