Magnetic Pseudodifferential Operators with Coefficients in $C^{\ast }$-Algebras

Abstract

In previous articles, a magnetic pseudodifferential calculus and a family of $C^{\ast }$-algebras associated with twisted dynamical systems were introduced and the connections between them have been established. We extend this formalism to symbol classes of Hörmander type with an $x$-behavior modeled by an abelian $C^{\ast }$-algebra. Some of these classes generate $C^{\ast }$-algebras associated with the twisted dynamical system. We show the relevance of these classes to the spectral analysis of pseudodifferential operators with anisotropic symbols and magnetic fields.