An affirmative answer to a core issue on limit operators

Publikationstyp
Journal Article
Date Issued
2014-04-03
Sprache
English
Author(s)
Lindner, Marko  orcid-logo
Seidel, Markus  
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/9524
Journal
Journal of functional analysis  
Volume
267
Issue
3
Start Page
901
End Page
917
Citation
Journal of functional analysis (3): 901-917 267 (2014)
Publisher DOI
10.1016/j.jfa.2014.03.002
Scopus ID
2-s2.0-84901684996
ArXiv ID
1401.1300v2
Publisher
Elsevier
An operator on an lแต–-space is called band-dominated if it can be approximated, in the operator norm, by operators with a banded matrix representation. It is known that a rich band-dominated operator is ๐“Ÿ-Fredholm (which is a generalization of the classical Fredholm property) if and only if all of its so-called limit operators are invertible and their inverses are uniformly bounded. We show that the condition on uniform boundedness is redundant in this statement.
Subjects
Band-dominated operator
Fredholm theory
Limit operator
Mathematics - Functional Analysis
Mathematics - Functional Analysis
Mathematics - Operator Algebras
DDC Class
510: Mathematik