Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Tracial oscillation zero and stable rank one (2112.14007v4)

Published 28 Dec 2021 in math.OA

Abstract: Let $A$ be a separable (not necessarily unital) simple $C*$-algebra with strict comparison. We show that if $A$ has tracial approximate oscillation zero then $A$ has stable rank one and the canonical map $\Gamma$ from the Cuntz semigroup of $A$ to the corresponding affine function space is surjective. The converse also holds. As a by-product, we find that a separable simple $C*$-algebra which has almost stable rank one must have stable rank one, provided it has strict comparison and the canonical map $\Gamma$ is surjective.

Summary

We haven't generated a summary for this paper yet.