A $C^*$-algebraic approach to the principal symbol II
Operator Algebras
2018-06-20 v1
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 , noncommutative tori and Moyal planes.
Keywords
Cite
@article{arxiv.1806.07015,
title = {A $C^*$-algebraic approach to the principal symbol II},
author = {Fedor Sukochev and Edward McDonald and Dmitriy Zanin},
journal= {arXiv preprint arXiv:1806.07015},
year = {2018}
}