Symmetrized trace and symmetrized determinant of odd class pseudo-differential operators (Q2270497)

The author considers the class of the odd logarithmic pseudo-differential operators on an odd-dimensional manifold. Locally, the symbols of the operators in this class are of the form \[ p(x,\eta)\sim c\log\eta+ \sum^\infty_{j=0} p_{m-j}(x,\eta) \] with \[ p_{m-j}(x,\lambda\eta)= \lambda^{m-j} p_{m-j}(x,\eta),\quad j= 0,1,\dots, \] for \(\lambda\in\mathbb{R}\), \(\lambda\neq 0\). The author introduces in this class a new definition of canonical trace. A related notion of determinant for elliptic pseudo-differential operators is also discussed.