a Poisson operator, $T$ a trace operator, and $S$ a pseudodifferential operator on $X'$. We assume that all are of order $\nu$. Details on the calculus can e.g. be found in [@G2].

As a first observation we note that for classical (one-step polyhomogeneous) $\psi $do’s $P$ of order $\nu $ on $\widetilde X$, the calculus of Boutet de Monvel requires $\nu \in\Bbb Z$ in order for the transmission condition to be satisfied at $\partial X$. The definition of the operators $G$, $K$ and $T$ (and, of course, $S$), however, extends readily to noninteger $\nu
$, so one can also ask for an extension of the canonical trace to operators of the form $$\pmatrix G & K\\ T&S
\endpmatrix ,\tag2.2$$ with pseudodifferential part equal to zero and all elements of order $\nu \in \Bbb R$.

We next fix an auxiliary operator: We let $P_1$ be a second-order strongly elliptic differential operator in $\widetilde E$ with scalar principal symbol, and denote by $P_{1,D}$ its Dirichlet realization on $X$. By possibly shifting the operator by a constant, we can assume that $P_1$ and $P_{1,\operatorname{D}}$ have positive lower bound, so that the resolvents $Q_\lambda =(P_1-\lambda )^{-1}$ and $R_\lambda =(P_{1,\operatorname{D}}-\lambda )^{-1}$ are defined for $\lambda 