$C^{\ast}$-algebraic approach to the principal symbol. III

Yuri Kordyukov; Fedor Sukochev; Dmitriy Zanin

doi:10.4171/jncg/553

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$C^{*}$ -algebraic approach to the principal symbol. III

Yuri Kordyukov
Ufa Federal Research Centre, Russian Academy of Sciences, Ufa, Russia
Fedor Sukochev
University of New South Wales, Kensington, Australia
Dmitriy Zanin
University of New South Wales, Kensington, Australia

$$C^{\ast}$-algebraic approach to the principal symbol. III cover$

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Abstract

We treat the notion of principal symbol mapping on a compact smooth manifold as a $*$ -homomorphism of $C^{*}$ -algebras. Principal symbol mapping is built from the ground, without referring to the pseudodifferential calculus on the manifold. Our concrete approach allows us to extend Connes trace theorem for compact Riemannian manifolds.

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Yuri Kordyukov, Fedor Sukochev, Dmitriy Zanin, $C^{*}$ -algebraic approach to the principal symbol. III. J. Noncommut. Geom. (2024), published online first

DOI 10.4171/JNCG/553