Xuanlong Fu

activity

20202026

most citedTracial approximation in simple C*-algebras

1 citations · 2 across the 5 of their papers we have counts for

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math.OA2026

Divisibility and Real Rank Zero

Xuanlong Fu

Let $A$ be a simple separable exact $C^{*}$ -algebra that has traces. We show the following existed regularity properties are equivalent: \quad(1) $l^{\infty} (A) / J_{A}$ has real rank zero…

math.OA2025

From Stable Rank One to Real Rank Zero: A Note on Tracial Approximate Oscillation Zero

Xuanlong Fu

We present a relation between stable rank one and real rank zero via the method of tracial oscillation. Let $A$ be a simple separable $C^{*}$ -algebra of stable rank one. We show that…

math.OA2021

Tracial approximate divisibility and stable rank one

Xuanlong Fu, Kang Li, Huaxin Lin

We show that every separable simple tracially approximately divisible $C^{*}$ -algebra has strict comparison, is either purely infinite, or has stable rank one. As a consequence, we s…

math.OA2021★ 1 cited

Non-amenable simple C*-algebras with tracial approximation

Xuanlong Fu, Huaxin Lin

We construct two types of unital separable simple $C^{*}$ -alebras $A_{z}^{C_{1}}$ and $A_{z}^{C_{2}},$ one is exact but not amenable, and the other is non-exact. Both have the same Elliott i…

math.OA2020★ 1 cited

Tracial approximation in simple C*-algebras

Xuanlong Fu, Huaxin Lin

We revisit the notion of tracial approximation for unital simple C*-algebras. We show that a unital simple separable C*-algebra A is asymptotically tracially in the class of C*-alg…