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<p>A compact quantum metric space is a unital <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13_2025_2182_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>-algebra equipped with a Lip-norm. We prove that the (infinite) tensor product of compact quantum metric spaces is a compact quantum metric space for any <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13_2025_2182_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>-norm on the algebraic tensor product.</p>

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Tensor products of compact quantum metric spaces

  • 期刊论文

  • 发表日期：

    2025年10月10日

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  • Botao Long,
  • Ghadir Sadeghi

摘要

A compact quantum metric space is a unital \(C^*\) C ∗ -algebra equipped with a Lip-norm. We prove that the (infinite) tensor product of compact quantum metric spaces is a compact quantum metric space for any \(C^*\) C ∗ -norm on the algebraic tensor product.