The index of a pair of projections on a Hilbert space was introduced in 1973 by Brown-Douglas-Filmore and connected to the integer quantum Hall effect by Avron-Seiler-Simon in 1994. For two orthogonal projections P,Q such that P-Q is compact, index(P,Q)=dimimP∩kerQ-dimimQ∩kerP. It is manifestly an integer, and enjoys norm and compactness stability, much like the related […]


