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Sufficiency of Favard's condition for a class of band-dominated operators on the axis \ud

By Simon N. Chandler-Wilde and Marko Lindner

Abstract

The purpose of this paper is to show that, for a large class of band-dominated operators on $\ell^\infty(Z,U)$, 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 $\ell^p(Z,U)$, regardless of $p\in[1,\infty]$, as the union of point spectra of its limit operators considered as acting on $\ell^p(Z,U)$.\ud \u

Topics: 510
Publisher: Elsevier
Year: 2008
OAI identifier: oai:centaur.reading.ac.uk:1158
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