On the essential spectrum of magnetic pseudodifferential operators
In [\textit{M.\,Mantoiu} and \textit{R.\,Purice}, J.~Math.\ Phys.\ 45, No.\,4, 1394--1417 (2004; Zbl 1068.81043)], the first two authors defined a gauge-covariant quantization for a particle in a magnetic field, extending the Weyl pseudodifferential calculus. In the present paper, the authors interpret the resulting pseudodifferential operators (associated with elliptic symbols and anisotropic potentials) as observables affiliated to an appropriate \(C^*\)-algebra. Using this approach, they obtain a decomposition of the essential spectrum of such an operator into a union of essential spectra of special operators prescribed by the asymptotic behavior of the magnetic field and potential. This leads to an extension of some localization results of \textit{W.\,O.\,Amrein, M.\,Mantoiu} and \textit{R.\,Purice} [Ann.\ Henri Poincaré 3, No.\,6, 1215--1232 (2002; Zbl 1029.81066)].
scientific article; zbMATH DE number 5126416