Infinite Matrices and their Finite Sections An Introduction to the Limit Operator Method

From the reviews:

“The book under review introduces the reader to one of the central themes concerning infinite matrices: approximation by matrices of finite size. It is written for a broad audience starting with graduate students in mathematics and above. … It is more introductory in nature and provides a very accessible summary of core themes, which are helpful in understanding properties of infinite matrices like Fredholmness, invertibility at infinity, stability and limit operators.” (G. Feichtinger, Monatshefte für Mathematik, Vol. 159 (4), March, 2010)