2024
DOI: 10.3934/math.2024967
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Interpolation unitarily invariant norms inequalities for matrices with applications

Mohammad Al-Khlyleh,
Mohammad Abdel Aal,
Mohammad F. M. Naser

Abstract: <abstract><p>Let $ A_j, B_j, P_j $, and $ Q_j \in M_{n}(\mathbb{C}) $, where $ j = 1, 2, \dots, m $. For a real number $ c \in [0, 1] $, we prove the following interpolation inequality:</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} {\left\vert\kern-0.1ex\left\vert\kern-0.1ex\left\vert {\sum\limits_{j = 1}^m {{A_j}{P_j}{Q_j}^*{B_j}^*} } \right\vert\kern-0.1ex\right\vert\kern-0.1ex\right\vert}^2 \leq {\left( {\max \left\{ {L,… Show more

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