## Rocky Mountain Journal of Mathematics

### The comparison properties and large subalgebra are inheritance

#### Abstract

Let $A$ be a an infinite dimensional stably finite unital simple separable exact ${\rm C^*}$-algebra. Let $B\subset A$ be a stably large subalgebra in $A$ such that $B$ has $m$-comparison of positive elements property (strong tracial $m$-comparison of positive elements property). Then $A$ has $m$-comparison of positive elements property (strong tracial $m$-comparison of positive elements property).

#### Article information

Source
Rocky Mountain J. Math., Volume 49, Number 6 (2019), 1857-1867.

Dates
First available in Project Euclid: 3 November 2019

https://projecteuclid.org/euclid.rmjm/1572746422

Digital Object Identifier
doi:10.1216/RMJ-2019-49-6-1857

Mathematical Reviews number (MathSciNet)
MR4027237

#### Citation

Fan, Qingzhai; Fang, Xiaochun; Zhao, Xia. The comparison properties and large subalgebra are inheritance. Rocky Mountain J. Math. 49 (2019), no. 6, 1857--1867. doi:10.1216/RMJ-2019-49-6-1857. https://projecteuclid.org/euclid.rmjm/1572746422

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