<p>We analyze a notion of <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2025_434_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">$C^$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-independence for <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2025_434_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">${\mathbb {Z}}_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-graded <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2025_434_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">$C^$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-algebras. We provide other notions of statistical independence for <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2025_434_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">${\mathbb {Z}}_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-graded von Neumann algebras and prove some relationships between them. We provide a characterization for the graded nuclearity property.</p>

$C^$-independence for ${\mathbb {Z}}_2$-graded $C^$-algebras

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2025年5月13日

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Maria Elena Griseta,
Paola Zurlo

摘要

We analyze a notion of $C^*$ $C^{*}$ -independence for ${\mathbb {Z}}_2$ $Z_{2}$ -graded $C^*$ $C^{*}$ -algebras. We provide other notions of statistical independence for ${\mathbb {Z}}_2$ $Z_{2}$ -graded von Neumann algebras and prove some relationships between them. We provide a characterization for the graded nuclearity property.

\(C^*\)-independence for \({\mathbb {Z}}_2\)-graded \(C^*\)-algebras

摘要

\(C^\)-independence for \({\mathbb {Z}}_2\)-graded \(C^\)-algebras