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.
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Schrohe, E. (1997). Wodzicki’s Noncommutative Residue and Traces for Operator Algebras on Manifolds with Conicai Singularities. In: Rodino, L. (eds) Microlocal Analysis and Spectral Theory. NATO ASI Series, vol 490. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5626-4_7
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