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<p>We study positive regular summability methods for bounded linear operators acting between extrapolation spaces. In particular, we show that the Banach–Saks property with respect to such summability methods is transferable from underlying families of Banach spaces to extrapolation spaces. The results obtained concern a large class of extrapolation spaces, including Zygmund spaces and the grand and small Lebesgue spaces.</p>

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Regular summability in extrapolation spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月31日

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  • Andrzej Kryczka

摘要

We study positive regular summability methods for bounded linear operators acting between extrapolation spaces. In particular, we show that the Banach–Saks property with respect to such summability methods is transferable from underlying families of Banach spaces to extrapolation spaces. The results obtained concern a large class of extrapolation spaces, including Zygmund spaces and the grand and small Lebesgue spaces.