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<p>We study the norm and the minimum modulus attainment sets of a bounded linear operator between Banach spaces. We illustrate several applications of such a study in the theory of norm-attaining operators, including complete characterizations of the norm-attaining operators and adjoint operators. We also present some sufficient conditions for the norm (minimum modulus) attainment of bounded linear operators and their adjoints. Furthermore, we obtain some new results on the quasi-norm attainment of bounded linear operators.</p>

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On the norm and the minimum modulus attainment of an operator and its adjoint

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Ankan Mishra,
  • Saikat Roy,
  • Debmalya Sain

摘要

We study the norm and the minimum modulus attainment sets of a bounded linear operator between Banach spaces. We illustrate several applications of such a study in the theory of norm-attaining operators, including complete characterizations of the norm-attaining operators and adjoint operators. We also present some sufficient conditions for the norm (minimum modulus) attainment of bounded linear operators and their adjoints. Furthermore, we obtain some new results on the quasi-norm attainment of bounded linear operators.