### Abstract

The Fredholmness of a band-dominated operator on l^{2}(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.

Original language | English (US) |
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Pages (from-to) | 221-238 |

Number of pages | 18 |

Journal | Integral Equations and Operator Theory |

Volume | 49 |

Issue number | 2 |

DOIs | |

State | Published - Jun 18 2004 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Algebra and Number Theory

### Cite this

*Integral Equations and Operator Theory*,

*49*(2), 221-238. https://doi.org/10.1007/s00020-003-1285-1

}

*Integral Equations and Operator Theory*, vol. 49, no. 2, pp. 221-238. https://doi.org/10.1007/s00020-003-1285-1

**Fredholm indices of band-dominated operators.** / Rabinovich, Vladimir S.; Roch, Steffen; Roe, John.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Fredholm indices of band-dominated operators

AU - Rabinovich, Vladimir S.

AU - Roch, Steffen

AU - Roe, John

PY - 2004/6/18

Y1 - 2004/6/18

N2 - The Fredholmness of a band-dominated operator on l2(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.

AB - The Fredholmness of a band-dominated operator on l2(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.

UR - http://www.scopus.com/inward/record.url?scp=2942535965&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2942535965&partnerID=8YFLogxK

U2 - 10.1007/s00020-003-1285-1

DO - 10.1007/s00020-003-1285-1

M3 - Article

AN - SCOPUS:2942535965

VL - 49

SP - 221

EP - 238

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 2

ER -