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<p>We showed two types of operator inequalities between the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_431_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\((n+1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>th residual relative operator entropy and the difference of the <i>n</i>th residual relative operator entropies. They are similar partially but have some differences. We investigate what these differences come from. Inequalities other than the previous ones are given through this process.</p>

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Inequalities among the nth residual relative operator entropies

  • 期刊论文

  • 发表日期：

    2025年3月22日

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  • Hiroaki Tohyama,
  • Eizaburo Kamei,
  • Masayuki Watanabe

摘要

We showed two types of operator inequalities between the \((n+1)\) ( n + 1 ) th residual relative operator entropy and the difference of the nth residual relative operator entropies. They are similar partially but have some differences. We investigate what these differences come from. Inequalities other than the previous ones are given through this process.