@inproceedings{1dfd97445ff64217ac22669a88833ba6,
title = "Finite sections of band-dominated operators on discrete groups",
abstract = "Let Γ be a finitely generated exact discrete group. We consider operators on Ɩ2(Γ) which are composed by operators of multiplication by a function in Ɩ∞(Γ) and by the operators of left-shift by elements of Γ. These operators generate a c∗ -subalgebra of (Ɩ2(Γ)) the elements of which we call band-dominated operators on Γ. We study the stability of the finite sections method for band-dominated operators with respect to a given generating system of Γ. Our approach is based on the equivalence of the stability of a sequence and the Fredholmness of an associated operator, and on Roe{\textquoteright}s criterion for the Fredholmness of a band-dominated operator on an exact discrete group, which we formulate in terms of limit operators. Special emphasis is paid to the quasicommutator ideal of the algebra generated by the finite sections sequences and to the stability of sequences in that algebra. For both problems, the sequence of the discrete boundaries plays an essential role.",
keywords = "Band-dominated operators, Discrete groups, Finite sections method, Group c-algebras, Limit operators, Stability",
author = "Rabinovich, {Vladimir S.} and Steffen Roch",
note = "Publisher Copyright: {\textcopyright} 2012 Springer Basel AG.; 20th International Workshop on Operator Theory and Applications, IWOTA 2009 ; Conference date: 21-09-2009 Through 25-09-2009",
year = "2012",
doi = "10.1007/978-3-0348-0346-5_15",
language = "Ingl{\'e}s",
isbn = "9783034803458",
series = "Operator Theory: Advances and Applications",
publisher = "Springer International Publishing",
pages = "239--253",
editor = "Ball, {Joseph A.} and Helton, {J. William} and Curto, {Ra{\'u}l E.} and Grudsky, {Sergei M.} and Ra{\'u}l Quiroga-Barranco and Vasilevski, {Nikolai L.}",
booktitle = "Recent Progress in Operator Theory and Its Applications",
}