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Abstract <p> It is proved that the summing basis in the classical James space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(J\)</EquationSource> </InlineEquation> has the random unconditional convergence property, whereas the canonical basis does not have this property. Necessary and sufficient conditions are also found under which an arbitrary subsequence of the canonical basis has the same property in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(J\)</EquationSource> </InlineEquation>. </p>

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On Properties of Bases in the James Space

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • S. V. Astashkin,
  • V. M. Ershov,
  • E. I. Zhugaleva

摘要

Abstract

It is proved that the summing basis in the classical James space \(J\) has the random unconditional convergence property, whereas the canonical basis does not have this property. Necessary and sufficient conditions are also found under which an arbitrary subsequence of the canonical basis has the same property in \(J\) .