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arXiv · 1806.07015

A $C^*$-algebraic approach to the principal symbol II

Fedor Sukochev·Edward McDonald·Dmitriy Zanin
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Abstract

We introduce an abstract theory of the principal symbol mapping for pseudodifferential operators extending the results of a preceding paper and providing a simple algebraic approach to the theory of pseudodifferential operators in settings important in noncommutative geometry. We provide a variant of Connes' trace theorem which applies to certain noncommutative settings, with a minimum of technical preliminaries. Our approach allows us to consider in a operators with non-smooth symbols, and we demonstrate the power of our approach by extending Connes' trace theorem to operators with non-smooth symbols in three examples: the Lie group $\mathrm{SU}(2)$, noncommutative tori and Moyal planes.

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Fedor Sukochev, Edward McDonald, Dmitriy Zanin. 2018-06-19. A $C^*$-algebraic approach to the principal symbol II. https://arxiv.org/abs/1806.07015

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