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<p>By introducing several new lemmas on the complementarity of closed subspaces in Banach spaces, we revisit the classical problem of determining when the product of relatively regular operators is itself relatively regular. Additionally, we provide sufficient conditions for a pair of operators that guarantee their relative regularity and the relative regularity of their product.</p>

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On relative regularity of operator products

  • 期刊论文

  • 发表日期：

    2025年9月12日

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  • Ayoub Ghorbel

摘要

By introducing several new lemmas on the complementarity of closed subspaces in Banach spaces, we revisit the classical problem of determining when the product of relatively regular operators is itself relatively regular. Additionally, we provide sufficient conditions for a pair of operators that guarantee their relative regularity and the relative regularity of their product.