Let <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2024_399_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\Omega $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation> be a class of C-algebras with the m-comparison property (respectively, the n-almost divisibility property, the weakly (k, n)-divisibility property). We show that any infinite-dimensional simple unital C-algebra in the class GTA<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2024_399_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\Omega $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation> (the class of C-algebras which can be generalized tracially approximated by the C-algebras in <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2024_399_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\Omega $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation>) has m-comparison (respectively, is <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2024_399_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="60" /> </InlineMediaObject> <EquationSource Format="TEX">$(2n+1)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-almost divisible, is weakly (k, 2n)-divisible).

Inheritance of certain comparison and divisibility properties for generalized tracially approximated C*-algebras

期刊论文
发表日期：

2025年1月12日

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Xiaochun Fang,
Zhongli Wang

摘要

Let $\Omega $ $Ω$ be a class of C*-algebras with the m-comparison property (respectively, the n-almost divisibility property, the weakly (k, n)-divisibility property). We show that any infinite-dimensional simple unital C*-algebra in the class GTA $\Omega $ $Ω$ (the class of C*-algebras which can be generalized tracially approximated by the C*-algebras in $\Omega $ $Ω$ ) has m-comparison (respectively, is $(2n+1)$ $(2 n + 1)$ -almost divisible, is weakly (k, 2n)-divisible).