Using 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 non-commutative
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 projections is in the calculus.Comment: 10 page
