Band-dominated Fredholm operators on discrete groups
\textit{V.\ S.\ Rabinovich, S.\ Roch} and \textit{B.\ Silbermann} [Integral Equations Oper.\ Theory 40, No.~3, 342--381 (2001; Zbl 1032.47051)] considered the \(C^{\ast}\)-algebra of band-dominated operators with operator-valued coefficients, a class of operators on the Hilbert space \(\ell^{2} (\mathbb{Z}^{n})\). They built a symbol calculus which provides a theoretical answer to the question whether or not a band-dominated operators is Fredholm. In the paper under review, the author extends the main results of the symbol calculus of [loc.~cit.] in the Hilbert space case. He replaces the group \(\mathbb{Z}^{n}\) by any finitely generated discrete group \(\Gamma\) which is exact in the sense of \(C^{\ast}\)-algebra theory.
band-dominated Fredholm operators with operator-valued coefficients
scientific article; zbMATH DE number 2162377