Toeplitz Operators and Poincaré Duality

Abstract

The study of matrices constant on all diagonals was introduced by Toeplitz [30]. Such matrices can be finite, semi-finite, or doubly-infinite. Aside from the profundity of results which have been obtained about such matrices the other amazing thing about them is the extent to which they occur in widely varied parts of mathematics, both pure and applied. Although several heuristic or even philosophical reasons could be advanced for this, we offer just one in this note and we concentrate entirely on the infinite cases.