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<p>We characterize surjective isometries on the unit spheres of complex Schreier spaces with <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>-convexifications, where <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\beta \in (0,1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>β</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. As an application, we prove that every surjective isometry between the unit spheres of these spaces admits a unique extension to a surjective real-linear isometry on the whole spaces. This yields a positive solution to Tingley’s problem for complex Schreier spaces with <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>-convexifications.</p>

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Tingley’s problem for complex Schreier spaces with \(\beta \)-convexifications

  • 期刊论文

  • 发表日期：

    2026年7月6日

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  • Ruidong Wang,
  • Jianglong Luo

摘要

We characterize surjective isometries on the unit spheres of complex Schreier spaces with \(\beta \) β -convexifications, where \(\beta \in (0,1)\) β ∈ ( 0 , 1 ) . As an application, we prove that every surjective isometry between the unit spheres of these spaces admits a unique extension to a surjective real-linear isometry on the whole spaces. This yields a positive solution to Tingley’s problem for complex Schreier spaces with \(\beta \) β -convexifications.