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<p>We prove that subhomogeneous continuous Banach bundles over compact metrizable spaces are equivalent to Hilbert bundles, while examples show that the metrizability assumption cannot be dropped completely. This complements the parallel statement for homogeneous bundles without the metrizability assumption, and generalizes the analogous result to the effect that subhomogeneous <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2025_432_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> bundles over compact metrizable spaces admit finite-index expectations.</p>

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Single and multi-valued Hilbert-bundle renormings

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月6日

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  • Alexandru Chirvasitu

摘要

We prove that subhomogeneous continuous Banach bundles over compact metrizable spaces are equivalent to Hilbert bundles, while examples show that the metrizability assumption cannot be dropped completely. This complements the parallel statement for homogeneous bundles without the metrizability assumption, and generalizes the analogous result to the effect that subhomogeneous \(C^*\) C ∗ bundles over compact metrizable spaces admit finite-index expectations.