Abstract
We introduce the index N(ω₁,ω₂) of a pair of pure states on a unital C*-algebra, which is a generalization of the notion of the index of a pair of projections on a Hilbert space. We then show that the Hall conductance associated with an invertible state ω of a two-dimensional interacting electronic system which is symmetric under U(1) charge transformation may be written as the index N(ω,ω_D), where ω_D is obtained from ω by inserting a unit of magnetic flux. This exhibits the integrality and continuity properties of the Hall conductance in the context of general topological features of N.