Nonpure (Non)Commutative Analysis, Geometry and Mechanics, part 1: differential and integral calculus
Operator Algebras
2022-09-28 v1 Differential Geometry
Abstract
We construct and study differential and integral calculus on the space of states of a C*-algebra by equipping it with a formal smooth structure. To achieve this goal we first concentrate on the space of nonpure states of a commutative C*-algebra as a guideline for the noncommutative case. In particular, we prove Stokes' theorem over the both commutative and noncommutative smooth Wasserstein space.
Keywords
Cite
@article{arxiv.2209.13169,
title = {Nonpure (Non)Commutative Analysis, Geometry and Mechanics, part 1: differential and integral calculus},
author = {Seyed Ebrahim Akrami},
journal= {arXiv preprint arXiv:2209.13169},
year = {2022}
}
Comments
Submitted to the Bulletin of Iranian Mathematical Society