Complex Analysis and Operator Theory

, Volume 2, Issue 4, pp 683–699 | Cite as

Finite Sections of Band-Dominated Operators: lp-Theory

Article

Abstract.

We propose an algebraic approach to the stability problem for the finite sections of general band-dominated operators acting on \(l^{p} = l^{p}({\mathbb{Z}})\) for 1 < p < ∞. This approach allows us to get new results which previously were known mainly for p = 2. One of the main results shows that a band-dominated operator is Fredholm if and only if the approximation numbers of its finite sections have a special behavior.

Mathematics Subject Classification (2000).

47B35 47B36 47A75 

Keywords.

Band-dominated operators finite sections approximation numbers 

Copyright information

© Birkhaeuser 2008

Authors and Affiliations

  1. 1.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany

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