Banach algebras of operator sequences (Q2914863)

The authors of the paper under review apply Banach algebra techniques for using operator sequences to approximate linear operators. For a given sequence \({\mathcal P}=\{P_n\}\) of projections, the authors introduce the notions of \({\mathcal P}\)-compactness, \({\mathcal P}\)-Fredholmness and \({\mathcal P}\)-strong convergence. These notions are used to generalize the finite section method. The authors obtain general results and consider applications.