M-elliptic pseudo-differential operators on L-P(R-n)

We construct the minimal and maximal extensions in L-p (R-n), 1 < p < infinity, for M-elliptic pseudo-differential operators initiated by Garello and Morando. We prove that they are equal and determine the domains of the minimal, and hence maximal, extensions of M-elliptic pseudo-differential operators. For M-elliptic pseudo-differential operators with constant coefficients, the spectra and essential spectra are computed. An application to quantization is given. (c) 2006 WILEY VCH Verlag GmbH & Co. KGaA, Weinheim.