Integral Equations and Operator Theory

, Volume 49, Issue 2, pp 221–238

Fredholm Indices of Band-Dominated Operators

Original paper

DOI: 10.1007/s00020-003-1285-1

Cite this article as:
Rabinovich, V.S., Roch, S. & Roe, J. Integr. equ. oper. theory (2004) 49: 221. doi:10.1007/s00020-003-1285-1

Abstract.

The Fredholmness of a band-dominated operator on \( l^2 (\mathbb{Z}) \) is closely related with the invertibility of its limit operators: the operator is Fredholm if and only if each of its limit operators is invertible and if the norms of their inverses are uniformly bounded. The goal of the present note is to show how the Fredholm index of a Fredholm band-dominated operator can be determined in terms of its limit operators.

Mathematics Subject Classification (2000).

Primary: 47A53Secondary: 46L80

Keywords.

Band-dominated operatorsFredholm indiceslimit operatorsK-theory in C*-algebrasrough kernel

Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.ESIME ZacatencoInstituto Politechnico NacionalMexico, D.F.Mexico
  2. 2.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  3. 3.Pennsylvania State UniversityUniversity ParkUSA