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Original Articles

Positive and real-positive solutions to the equation axa*=c in C*-algebras

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Pages 535-543 | Received 07 Aug 2006, Accepted 23 Jan 2007, Published online: 09 Oct 2007

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Chong-Quan Zhang, Qing-Wen Wang, Andrii Dmytryshyn & Zhuo-Heng He. (2024) Investigation of some Sylvester-type quaternion matrix equations with multiple unknowns. Computational and Applied Mathematics 43:4.
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Hranislav Stanković. (2023) Solvability of $$A_iXB_i=C_i,\, i=\overline{1,2},$$ with applications to inequality $$C{\mathop {\le }\limits ^{*}}AXB$$. Advances in Operator Theory 8:2.
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Xin Liu & Yang Zhang. 2023. Matrix and Operator Equations and Applications. Matrix and Operator Equations and Applications 139 183 .
Z. Niazi Moghani, M. Mohammadzadeh Karizaki & M. Khanehgir. (2021) Solutions of the Sylvester Equation in C*-Modular Operators. Ukrainian Mathematical Journal 73:3, pages 414-432.
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M. Khanehgir, Z. N. Moghani & M. Mohammadzadeh Karizaki. (2021) Solutions of Sylvester equation in -modular operators. Ukrains’kyi Matematychnyi Zhurnal 73:3, pages 354-369.
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Guangjing Song & Shaowen Yu. (2018) Nonnegative definite and Re-nonnegative definite solutions to a system of matrix equations with statistical applications. Applied Mathematics and Computation 338, pages 828-841.
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Biljana Radi?i?Branko Male?evi?. (2014) Some Considerations in Relation to the Matrix Equation AXB =?C. Mediterranean Journal of Mathematics 11:3, pages 841-856.
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Guang-Jing Song & Ming Chen. (2013) Common nonnegative definite solutions of some classical matrix equations. Journal of Applied Mathematics and Computing 44:1-2, pages 83-97.
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QingWen Wang & ZhuoHeng He. (2013) A system of matrix equations and its applications. Science China Mathematics 56:9, pages 1795-1820.
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Chunyuan Deng. (2013) On the solutions of operator equation . Journal of Mathematical Analysis and Applications 398:2, pages 664-670.
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Chang-Zhou Dong, Qing-Wen Wang & Yu-Ping Zhang. (2012) The common positive solution to adjointable operator equations with an application. Journal of Mathematical Analysis and Applications 396:2, pages 670-679.
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Qing-Wen Wang & Chang-Zhou Dong. (2010) Positive solutions to a system of adjointable operator equations over Hilbert -modules . Linear Algebra and its Applications 433:7, pages 1481-1489.
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M. Laura Arias & M. Celeste Gonzalez. (2010) Positive solutions to operator equations . Linear Algebra and its Applications 433:6, pages 1194-1202.
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Xiaochun Fang & Jing Yu. (2010) Solutions to Operator Equations on Hilbert C*-Modules II. Integral Equations and Operator Theory 68:1, pages 23-60.
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Yongge Tian. (2010) Equalities and inequalities for inertias of hermitian matrices with applications. Linear Algebra and its Applications 433:1, pages 263-296.
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Xiaochun Fang, Jing Yu & Hongliang Yao. (2009) Solutions to operator equations on Hilbert -modules . Linear Algebra and its Applications 431:11, pages 2142-2153.
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Bing Zheng, Lijuan Ye & Dragana S. Cvetkovic-Ilic. (2009) The *congruence class of the solutions of some matrix equations. Computers & Mathematics with Applications 57:4, pages 540-549.
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Qingxiang Xu, Lijuan Sheng & Yangyang Gu. (2008) The solutions to some operator equations. Linear Algebra and its Applications 429:8-9, pages 1997-2024.
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Qingxiang Xu. (2008) Common hermitian and positive solutions to the adjointable operator equations , . Linear Algebra and its Applications 429:1, pages 1-11.
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Qingxiang Xu & Lijuan Sheng. (2008) Positive semi-definite matrices of adjointable operators on Hilbert -modules . Linear Algebra and its Applications 428:4, pages 992-1000.
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