2001
DOI: 10.1007/bf01299850
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Band-dominated operators with operator-valued coefficients, their Fredholm properties and finite sections

Abstract: The central theme of the present paper are band and band-dominated operators, i.e. norm limits of band operators. In the first part, we generalize the results from [24] and [25] concerning the Fredholm properties of band-dominated operators and the applicability of the finite section method to the case of operators with operator-valued coefficients. We characterize these properties in terms of the limit operators of the given band-dominated operator. The main objective of the second part is to apply these resu… Show more

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Cited by 58 publications
(54 citation statements)
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“…One can easily check the following properties of limit operators (cf., e.g., [3, Proposition 6.1], [17,Proposition 2.12]). A, B, A n ∈ B(L 2 (Π)), n ∈ N, and τ ∈ {0, ∞}.…”
Section: Canonical Form Of Local Algebrasmentioning
confidence: 99%
“…One can easily check the following properties of limit operators (cf., e.g., [3, Proposition 6.1], [17,Proposition 2.12]). A, B, A n ∈ B(L 2 (Π)), n ∈ N, and τ ∈ {0, ∞}.…”
Section: Canonical Form Of Local Algebrasmentioning
confidence: 99%
“…We also learned of very recent work of Rabinovich [66], based in part on [47,61,64,65,67,68], using the theory of Fredholm operators to obtain results on essential spectrum as a union of spectra of suitable limits at infinity.…”
Section: Introductionmentioning
confidence: 99%
“…In Section 2, we recall some auxiliary material concerning the Wiener algebra of discrete operators on Z N and the limit operators method. Our presentation will follow the papers [20,21]. A comprehensive account of this material can be found in [22].…”
Section: Introductionmentioning
confidence: 99%