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<p>In this note, we introduce the notion of <i>P</i>-generalized Cartesian decomposition of operators in a semi-Hilbertian space induced by a positive operator <i>P</i> acting on a Hilbert space. Using this we obtain several generalizations of known <i>P</i>-numerical radius inequalities, which improve on the existing ones. Furthermore, we discuss characterizations for the equality of existing <i>P</i>-numerical radius inequalities.</p>

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A notion of the Cartesian decomposition and P-numerical radius bounds

  • 期刊论文

  • 发表日期：

    2025年7月9日

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  • Somdatta Barik,
  • Pintu Bhunia,
  • Kallol Paul

摘要

In this note, we introduce the notion of P-generalized Cartesian decomposition of operators in a semi-Hilbertian space induced by a positive operator P acting on a Hilbert space. Using this we obtain several generalizations of known P-numerical radius inequalities, which improve on the existing ones. Furthermore, we discuss characterizations for the equality of existing P-numerical radius inequalities.