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

2018/06/19 by Sukochev, Fedor, McDonald, Edward, Zanin, Dmitriy · 1 citation
#58B34 #58J40 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1806.07015

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 SU(2), noncommutative tori and Moyal planes.

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