Banach algebras of structured matrix sequences

We discuss the asymptotic behavior of matrix sequences belonging to a special class of non-commutative Banach algebras and study, in particular, the stability, and more general the Fredholm property of such sequences. The abstract results are applied to finite sections of band-dominated operators, e...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 430; no. 4; pp. 1243 - 1281
Main Authors Seidel, Markus, Silbermann, Bernd
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.02.2009
Elsevier
Subjects
47A58
47B36
47N40
65J10
[formula omitted]-splitting-property
Algebra
Approximation numbers
Band-dominated operators
Exact sciences and technology
Finite sections
Functional analysis
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematics
Matrix sequences
Sciences and techniques of general use
47N40
Approximation numbers
47B36
Band-dominated operators
Finite sections
47A58
k-splitting-property
65J10
Matrix sequences
k-Splitting-property
Matrix algebra
Asymptotic behavior
Band matrix
Banach algebra
Non commutative algebra
Structured matrix
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Summary:We discuss the asymptotic behavior of matrix sequences belonging to a special class of non-commutative Banach algebras and study, in particular, the stability, and more general the Fredholm property of such sequences. The abstract results are applied to finite sections of band-dominated operators, especially in the case lp(Z), 1⩽p⩽∞.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2008.10.021