Options
Sufficiency of Favard's condition for a class of band-dominated operators on the axis
Publikationstyp
Journal Article
Date Issued
2008-02-15
Sprache
English
Author(s)
Journal
Volume
254
Issue
4
Start Page
1146
End Page
1159
Citation
Journal of Functional Analysis 254 (4): 1146-1159 (2008-02-15)
Publisher DOI
Scopus ID
The purpose of this paper is to show that, for a large class of band-dominated operators on ℓ∞ (Z, U), with U being a complex Banach space, the injectivity of all limit operators of A already implies their invertibility and the uniform boundedness of their inverses. The latter property is known to be equivalent to the invertibility at infinity of A, which, on the other hand, is often equivalent to the Fredholmness of A. As a consequence, for operators A in the Wiener algebra, we can characterize the essential spectrum of A on ℓp (Z, U), regardless of p ∈ [1, ∞], as the union of point spectra of its limit operators considered as acting on ℓ∞ (Z, U).
Subjects
Favard condition
Fredholm operator
Limit operator
Wiener algebra
DDC Class
510: Mathematik