2008 | OriginalPaper | Buchkapitel
On Finite Sections of Band-dominated Operators
verfasst von : Vladimir S. Rabinovich, Steffen Roch, Bernd Silbermann
Erschienen in: Operator Algebras, Operator Theory and Applications
Verlag: Birkhäuser Basel
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In an earlier paper we showed that the sequence of the finite sections
P
n
AP
n
of a band-dominated operator
A
on
l
p
(ℤ) is stable if and only if the operator
A
is invertible, every limit operator of the sequence (
P
n
AP
n
) is invertible, and if the norms of the inverses of the limit operators are uniformly bounded. The purpose of this short note is to show that the uniform boundedness condition is redundant.