Invertibility of matrix type operators of infinite order with exponential off-diagonal decay

Abstract

© 2019 Elsevier Inc. We analyse various exponential off-diagonal decay rates of the elements of infinite matrices and their inverses. It is known that such decay of the elements of an infinite matrix does not imply inverse–closeness, i.e. the inverse, if exists, does not have the same order of decay. We discuss some consequences and extensions of this result.