Magnetic pseudodifferential operators with coefficients in C*-algebras

Abstract

In previous articles, a magnetic pseudodifferential 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 modelized 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 pseudodifferential operators with anisotropic symbols and magnetic fields.

23 pages

References in corpus (4)

• The Magnetic Weyl Calculus
• Magnetic Pseudodifferential Operators
• Localizations at infinity and essential spectrum of quantum Hamiltonians: I. General theory
• Quantum Magnetic Algebra and Magnetic Curvature

Cited by in corpus (8)

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• On the regularity of the Hausdorff distance between spectra of perturbed magnetic Hamiltonians
• Magnetic pseudodifferential operators represented as generalized Hofstadter-like matrices
• Index pairings for ${\mathbb{R}}^n$-actions and Rieffel deformations
• Positive Quantization in the Presence of a Variable Magnetic Field
• Rieffel's pseudodifferential calculus and spectral analysis of quantum Hamiltonians