关于算子的对数次控制形式 Audenaert不等式的一个推广
On a Logmajorization Version of Audenaert’s Inequality for Operators
摘要: 本文在半有限 von Neumann 代数的情形下，研究了一类与 Audenaert 不等式相关的对数次控 制不等式。 特别地，我们还将此类不等式推广到了扇形算子的情形。
Abstract: In the setting of semifinite von Neumann algebras, we study a class of log-majorization inequalities related to the Audenaert inequality. In particular, we extend such inequal- ities to the case of sectorial operators.
文章引用：李赞, 韩亚洲. 关于算子的对数次控制形式 Audenaert不等式的一个推广[J]. 应用数学进展, 2026, 15(5): 284-298. https://doi.org/10.12677/AAM.2026.155229

参考文献

[1] Wang, Y. and Shao, J. (2021) Some Logarithmic Submajorisations and Determinant Inequal- ities for Operators with Numerical Ranges in a Sector. Annals of Functional Analysis, 12, Article No. 27. [Google Scholar] [CrossRef] 
[2] Hoa, D.T. (2016) An Inequality for t-Geometric Means. Mathematical Inequalities & Applica- tions, 19, 765-768. [Google Scholar] [CrossRef] 
[3] Bourin, J. (2009) Matrix Subadditivity Inequalities and Block-Matrices. International Journal of Mathematics, 20, 679-691. [Google Scholar] [CrossRef] 
[4] Hayajneh, S. and Kittaneh, F. (2013) Trace Inequalities and a Question of Bourin. Bulletin of the Australian Mathematical Society, 88, 384-389. [Google Scholar] [CrossRef] 
[5] Audenaert, K. (2015) A Norm Inequality for Pairs of Commuting Positive Semidefinite Matri- ces. The Electronic Journal of Linear Algebra, 30, 80-84. [Google Scholar] [CrossRef] 
[6] Bikchentaev, A.M., Kittaneh, F., Moslehian, M.S. and Seo, Y. (2024) Trace Inequalities: For Matrices and Hilbert Space Operators. Springer, 332 p.
[7] Hayajneh, S. and Kittaneh, F. (2025) A Log-Majorization Version of Audenaert’s Inequality. Journal of Mathematical Analysis and Applications, 548, Article ID: 129372. [Google Scholar] [CrossRef] 
[8] Tan, F. and Che, H. (2019) Inequalities for Sector Matrices and Positive Linear Maps. The Electronic Journal of Linear Algebra, 35, 418-423. [Google Scholar] [CrossRef] 
[9] 许全华, 吐尔德别克, 陈泽乾. 算子代数与非交换Lp号论[M]. 北京: 科学出版社, 2010.
[10] Dodds, P.G., Dodds, T.K., Sukochev, F.A. and Zanin, D. (2020) Logarithmic Submajorization, Uniform Majorization and H¨older Type Inequalities for τ -Measurable Operators. Indagationes Mathematicae, 31, 809-830. [Google Scholar] [CrossRef] 
[11] Fack, T. and Kosaki, H. (1986) Generalized s-Numbers of τ -Measurable Operators. Pacific Journal of Mathematics, 123, 269-300. [Google Scholar] [CrossRef] 
[12] Hiai, F. and Kosaki, H. (2021) Connections of Unbounded Operators and Some Related Topics: Von Neumann Algebra Case. International Journal of Mathematics, 32, Article ID: 2150024. [Google Scholar] [CrossRef] 
[13] Kubo, F. and Ando, T. (1980) Means of Positive Linear Operators. Mathematische Annalen, 246, 205-224. [Google Scholar] [CrossRef] 
[14] Lawson, J., Lee, H. and Lim, Y. (2012) Weighted Geometric Means. Forum Mathematicum, 24, 1067-1090. [Google Scholar] [CrossRef] 
[15] Kosaki, H. (1992) An Inequality of Araki-Lieb-Thirring (Von Neumann Algebra Case). Pro- ceedings of the American Mathematical Society, 114, 477-481. [Google Scholar] [CrossRef] 
[16] Bikchentaev, A.M. (2017) On τ -Compactness of Products of τ -Measurable Operators. Inter- national Journal of Theoretical Physics, 56, 3819-3830. [Google Scholar] [CrossRef] 
[17] Han, Y.Z. and Yan, C. (2021) Harnack Type Inequalities for Operators in Logarithmic Subma- jorisation. Operators and Matrices, 15, 1109-1129. [Google Scholar] [CrossRef] 

为你推荐