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On Semi-Fredholm Band-Dominated Operators

Abstract

In this paper we study the semi-Fredholm property of band-dominated operators A and prove that it already implies the Fredholmness of A in all cases where this is not disqualified by obvious reasons. Moreover, this observation is applied to show that the Fredholmness of a band-dominated operator already follows from the surjectivity of all its limit operators.

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Correspondence to Markus Seidel.

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Seidel, M. On Semi-Fredholm Band-Dominated Operators. Integr. Equ. Oper. Theory 83, 35–47 (2015). https://doi.org/10.1007/s00020-015-2219-4

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  • DOI: https://doi.org/10.1007/s00020-015-2219-4

Mathematics Subject Classification

  • Primary 47A53
  • Secondary 47L10
  • 47B36
  • 46E40

Keywords

  • Semi-Fredholm operator
  • band-dominated operator
  • limit operator
  • operator spectrum