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<p>We study the reduced minimum of a bounded linear operator between Banach spaces with special reference to Hilbert spaces. We also study reduced minimum attaining operators between Banach spaces. We prove that for any Banach space <i>Y</i>, every bounded linear operator between Banach spaces <i>X</i> and <i>Y</i> attains the reduced minimum if and only if <i>X</i> is finite dimensional. Finally, we study the reduced minimum attainment set of an operator and characterize the reflexive property of a Banach space with the help of the reduced minimum attainment set of a rank-one operator.</p>

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On reduced minimum attaining operators

  • 期刊论文

  • 发表日期：

    2026年1月12日

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  • Uday Shankar Chakraborty

摘要

We study the reduced minimum of a bounded linear operator between Banach spaces with special reference to Hilbert spaces. We also study reduced minimum attaining operators between Banach spaces. We prove that for any Banach space Y, every bounded linear operator between Banach spaces X and Y attains the reduced minimum if and only if X is finite dimensional. Finally, we study the reduced minimum attainment set of an operator and characterize the reflexive property of a Banach space with the help of the reduced minimum attainment set of a rank-one operator.