Abstract
Li (Algebra 71:2823–2838, 2023) recently obtained several improvements on some partial trace inequalities for positive semidefinite block matrices. In this note, we present analogous partial trace inequalities involving partial transpose of positive semidefinite block matrix. The inequalities we show could be regarded as complements of Li’s results. In addition, some new partial trace inequalities for partial transpose of positive semidefinite block matrix are included.
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Acknowledgements
The work is supported by National Natural Science Foundation (Grant no. 12261030), Hainan Provincial Natural Science Foundation for High-level Talents (Grant no. 123RC474), Hainan Provincial Natural Science Foundation of China (Grant no. 124RC503), the Hainan Provincial Graduate Innovation Research Program (Grant nos. Qhys2022-246, Qhys2023-383, Qhys2023-385), the Key Laboratory of Computational Science and Application of Hainan Province.
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JY wrote the main manuscript text and HX gave some proofs of several theorems. All authors reviewed the manuscript
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Yang, J., Xu, H. Partial trace inequalities for partial transpose of positive semidefinite block matrices. Positivity 28, 21 (2024). https://doi.org/10.1007/s11117-024-01039-2
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DOI: https://doi.org/10.1007/s11117-024-01039-2