Original paper

Integral Equations and Operator Theory

, Volume 49, Issue 2, pp 221-238

Fredholm Indices of Band-Dominated Operators

  • Vladimir S. RabinovichAffiliated withESIME Zacatenco, Instituto Politechnico Nacional Email author 
  • , Steffen RochAffiliated withFachbereich Mathematik, Technische Universität Darmstadt Email author 
  • , John RoeAffiliated withPennsylvania State University Email author 

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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: 47A53 Secondary: 46L80

Keywords.

Band-dominated operators Fredholm indices limit operators K-theory in C*-algebras rough kernel