Closure of the set of pseudodifferential operators (Q424741)

The author gives a characterization of the closure in \({\mathcal L}(L^2)\) of the algebra of the pseudo-differential operators with symbol in \(S^0_{0,0}\). The characterization is provided in terms of representations of the Heisenberg group \(H_n\) in the space \({\mathcal L}(L^2)\). A similar result has been given for the Schatten classes, cf. \textit{C. Rondeaux} [Ann. Sci. Éc. Norm. Supér. (4) 17, 67--81 (1984; Zbl 0574.47032)].