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<p>We associate two specific projective systems of probability spaces to any Tsirelson convolution system. If the corresponding projective limit (in the sense of Bochner) exists, we say that the system is convergent in the first case and <i>K</i>-convergent in the second. It is shown that convergent convolution systems give rise to continuous products of probability spaces, while <i>K</i>-convergent systems lead to flow systems. We then investigate the relationship between convergence and <i>K</i>-convergence, as well as their connections to two-parameter product systems of Hilbert spaces.</p>

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Convergence of Tsirelson Convolution Systems of Probability Spaces

  • 期刊论文

  • 发表日期：

    2026年7月18日

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  • Remus Floricel,
  • Patrick Melanson

摘要

We associate two specific projective systems of probability spaces to any Tsirelson convolution system. If the corresponding projective limit (in the sense of Bochner) exists, we say that the system is convergent in the first case and K-convergent in the second. It is shown that convergent convolution systems give rise to continuous products of probability spaces, while K-convergent systems lead to flow systems. We then investigate the relationship between convergence and K-convergence, as well as their connections to two-parameter product systems of Hilbert spaces.