We consider the pseudo - differential operator
$$Jv=(1+i\,a(x)\,(1-\Delta)^{-1}\,a(x))\,v$$Studying the work of Camille Laurent,"Global controllability and stabilization for the nonlinear Schrodinger equation on some compact manifolds of dimension 3," SIAM J. Math. Anal 42 no. 2, pp. 785 -832, 2010, the author says that $J$ is a pseudo - differential operator of order zero?
How am I prove this fact?