English

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