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<p>The set of partial isometries in a <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13324_2025_1028_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(W^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>W</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-algebra possesses a structure of Banach Lie groupoid. In this paper, the differential structure on the set of partial isometries over the restricted Grassmannian is constructed, which makes it into a Banach Lie groupoid.</p>

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Banach Lie groupoid of partial isometries over the restricted Grassmannian

  • 期刊论文

  • 发表日期：

    2025年2月8日

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  • Tomasz Goliński,
  • Grzegorz Jakimowicz,
  • Aneta Sliżewska

摘要

The set of partial isometries in a \(W^*\) W ∗ -algebra possesses a structure of Banach Lie groupoid. In this paper, the differential structure on the set of partial isometries over the restricted Grassmannian is constructed, which makes it into a Banach Lie groupoid.