English

Differential operators on C*-algebras and applications to smooth functional calculus and Schwartz functions on the tangent groupoid

Operator Algebras 2024-09-04 v2 K-Theory and Homology

Abstract

We introduce the notion of a differential operator on C*-algebras. This is a noncommutative analogue of a differential operator on a smooth manifold. We show that the common closed domain of all differential operators is closed under smooth functional calculus. As a corollary, we show that Schwartz functions on Connes tangent groupoid are closed under smooth functional calculus.

Keywords

Cite

@article{arxiv.2210.08670,
  title  = {Differential operators on C*-algebras and applications to smooth functional calculus and Schwartz functions on the tangent groupoid},
  author = {Omar Mohsen},
  journal= {arXiv preprint arXiv:2210.08670},
  year   = {2024}
}

Comments

I changed the article following the referee's remarks (including a change to the title). To appear in Journal of Functional analysis