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