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<p>We investigate the notion of quasi-invariant states introduced in [<CitationRef CitationID="CR2">2</CitationRef>] from an analytic viewpoint. We give the structures of quasi-invariant states with uniformly bounded cocycles. As a consequence, we can apply a Theorem of Kovács and Szücs to get a conditional expectation on fixed points and another of St<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="220_2025_5304_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(\o \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">ø</mi> </math></EquationSource> </InlineEquation>rmer to get an invariant semifinite trace under extra assumptions.</p>

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Quasi-invariant States with Uniformly Bounded Cocycles

  • 期刊论文

  • 发表日期：

    2025年5月21日

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  • Ameur Dhahri,
  • Éric Ricard

摘要

We investigate the notion of quasi-invariant states introduced in [2] from an analytic viewpoint. We give the structures of quasi-invariant states with uniformly bounded cocycles. As a consequence, we can apply a Theorem of Kovács and Szücs to get a conditional expectation on fixed points and another of St \(\o \) ø rmer to get an invariant semifinite trace under extra assumptions.