Nonpure (Non)Commutative Analysis, Geometry and Mechanics, part 1: differential and integral calculus

2022/09/27 by Akrami, Seyed Ebrahim
#58B34 #58C20 #Differential Geometry (math.DG) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2209.13169

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.

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