Noncommutative residue of projections in Boutet de Monvel’s calculus

Abstract

Employing results by Melo, Nest, Schick and Schrohe on the K-theory of Boutet de Monvel’s calculus of boundary value problems, we show that the noncommutative residue introduced by Fedosov, Golse, Leichtnam and Schrohe vanishes on projections in the calculus. This partially answers a question raised in a recent collaboration with Grubb, namely whether the residue is zero on sectorial projections for boundary value problems: This is confirmed to be true when the sectorial projection is in the calculus.