Wodzicki’s Noncommutative Residue and Traces for Operator Algebras on Manifolds with Conicai Singularities

Abstract

In 1984 M. Wodzicki found a trace on the algebra Ψ cl (M) of all classical pseudodifferential operators on a closed compact manifold M; he called it the noncommutative residue. This trace vanishes on the ideal Ψ–∞ (M) of smoothing operators; it even is the unique trace (up to constant multiples) on Ψ cl (M)/ Ψ–∞ (M), provided M is connected and dim M > 1.