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<p>This paper investigates the interaction between RH-regular four-dimensional matrices and block-stretched double sequences, with a focus on Pringsheim limit point preservation. We introduce the “Ordered Block Decomposition Property” for double sequences and demonstrate that RH-regular matrices lacking this property fail to preserve limit points, even for bounded sequences. By constructing block-finite matrices with <i>P</i>-null differences, we establish that RH-regularity alone is insufficient to ensure limit preservation under block transformations.</p>

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Pringsheim limit preservation for block-stretched double sequences via RH-regular matrices

  • 期刊论文

  • 发表日期：

    2025年6月24日

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  • Sami M. Hamid,
  • Richard F. Patterson

摘要

This paper investigates the interaction between RH-regular four-dimensional matrices and block-stretched double sequences, with a focus on Pringsheim limit point preservation. We introduce the “Ordered Block Decomposition Property” for double sequences and demonstrate that RH-regular matrices lacking this property fail to preserve limit points, even for bounded sequences. By constructing block-finite matrices with P-null differences, we establish that RH-regularity alone is insufficient to ensure limit preservation under block transformations.