Fredholm indices of band-dominated operators

Vladimir S. Rabinovich; Steffen Roch; John Roe

doi:10.1007/s00020-003-1285-1

Fredholm indices of band-dominated operators

Vladimir S. Rabinovich, Steffen Roch, John Roe

Mathematics

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	221-238
Number of pages	18
Journal	Integral Equations and Operator Theory
Volume	49
Issue number	2
DOIs	https://doi.org/10.1007/s00020-003-1285-1
State	Published - 2004

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory

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10.1007/s00020-003-1285-1

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abstract = "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.",

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AU - Rabinovich, Vladimir S.

AU - Roch, Steffen

AU - Roe, John

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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.

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Fredholm indices of band-dominated operators

Abstract

All Science Journal Classification (ASJC) codes

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