On the noncommutative residue for projective pseudodifferential operators (Q355072)

The authors define the Wodzicki residue for projective pseudodifferential operators and prove that it vanishes on zero-order projections in the case the dimension of the manifold is odd. Basic reference for the authors is the work of \textit{V. Mathai} et al. [J. Differ. Geom. 74, No. 2, 265--292 (2006; Zbl 1115.58021)]. With respect to that paper, here the definition of projective pseudodifferential operator is reconsidered in terms of convolution bundles. This allows an equivalent definition of Wodzicki residue.NEWLINENEWLINE In such a setting, the computation of the residue can be reduced to a model, namely to positive projections of generalized Dirac operators, for which it is known that the residue density vanishes, cf. \textit{T. P. Branson} and \textit{P. B. Gilkey} [J. Funct. Anal. 108, No. 1, 47--87 (1992; Zbl 0756.58048)].