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Volume 46, Issue 4, 2010, pp. 755–788
DOI: 10.2977/PRIMS/25

Published online: 2010-11-18

Magnetic Pseudodifferential Operators with Coefficients in C*-Algebras

Max Lein[1], Marius Măntoiu[2] and Serge Richard[3]

(1) TU München, Garching Bei München, Germany
(2) Universidad de Chile, Santiago, Chile
(3) Université Claude Bernard Lyon 1, Villeurbanne, France

In previous articles, a magnetic pseudodi erential calculus and a family of C*-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*-algebra. Some of these classes generate C*-algebras associated with the twisted dynamical system.We show the relevance of these classes to the spectral analysis of pseudodi erential operators with anisotropic symbols and magnetic elds.

Keywords: magnetic field, pseudodifferential operator, C*-algebra, affiliation, essential spectrum, symbol class, twisted crossed-product, Ψ*-algebra

Lein Max, Măntoiu Marius, Richard Serge: Magnetic Pseudodifferential Operators with Coefficients in C*-Algebras. Publ. Res. Inst. Math. Sci. 46 (2010), 755-788. doi: 10.2977/PRIMS/25