Pseudo-differential Operators and Regularity of Spectral Triples

Details Pseudo-differential Operators and Regularity of Spectral Triples Pseudo-differential Operators and Regularity of Spectral Triples

2009-11-04

arxiv.org/abs/0911.0816v4

Fields Communications Series, Volume 61 - "Perspectives on Noncommutative Geometry", 2011, pp. 153 - 163

Mathematics

Operator Algebras

typos corrected; to appear in the Fields Institute Communications

Scientific paper

We introduce a notion of an algebra of generalized pseudo-differential
operators and prove that a spectral triple is regular if and only if it admits
an algebra of generalized pseudo-differential operators. We also provide a
self-contained proof of the fact that the product of regular spectral triples
is regular.

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