| 刘景,吴德玉,阿拉坦仓.Hilbert C*-模上具有伴随的2×2模映射矩阵的范数与数值半径估计[J].数学年刊A辑,2025,46(4):351~366 |
| Hilbert C*-模上具有伴随的2×2模映射矩阵的范数与数值半径估计 |
| The Estimations of the Norm and the Numerical Radius of Adjointable 2 × 2 Matrices on Hilbert C*-modules |
| Received:June 11, 2025 Revised:November 25, 2025 |
| DOI：10.16205/j.cnki.cama.2025.0023 |
| 中文关键词: 数值半径 Cartesian分解 Buzano不等式 Hilbert C*-模 |
| 英文关键词:Numerical radius Cartesian decomposition Buzano’s inequality Hilbert C*-module |
| 基金项目:国家自然科学基金(No. 12561022) 内蒙古自然科学基金 (No. 2022ZD05) |
| Author Name | Affiliation | | LIU Jing | School of Mathematical Sciences, Baotou Teachers’ College, Baotou 014030, Inner Mongolia, China
School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China. | | WU Deyu | School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China. | | Alatancang | School of Mathematical Sciences, Inner Mongolia Normal University, Hohhot 010022, China. |
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| 中文摘要: |
| 给出了Hilbert C*-模上具有伴随的2×2模映射矩阵的范数上界，进一步利用具有伴随的模映射的Cartesian分解，得到了具有伴随的模映射数值半径的下界，即ω??2(T) ≥ 1/8[max{∥T+T*∥4,∥T-T*∥4}+3∥T+T*∥2∥T-T*∥2]1/2和ω??2(T) ≥ 1/4[max{∥Re(T)+Im(T)∥4,∥Re(T)-Im(T)∥4}+3∥Re(T)+Im(T)∥2∥Re(T)-Im(T)∥2]1/2，其中Re(T)=(T+T*)/2和Im(T)=(T-T*)/2i分别为T的实部和虚部。最后利用Buzano不等式得到了Hilbert C*-模上具有伴随的2×2模映射矩阵的数值半径上界。此外，当Hilbert C*-模退化为Hilbert空间且参数取特殊值时，本文结论改进了Bani-Domi W和Kittaneh F得到的Hilbert空间上2×2有界线性算子矩阵的数值半径上界相关结果。 |
| 英文摘要: |
| In this paper, the upper bounds of the norm of adjointable 2 × 2 matrices on the Hilbert C*-module are given. Furthermore, by utilizing the Cartesian decomposition of adjointable maps, the lower bounds of the numerical radius of adjointable maps are derived. Namely ω??2(T) ≥ 1/8[max{∥T+T*∥4,∥T-T*∥4}+3∥T+T*∥2∥T-T*∥2]1/2 and ω??2(T) ≥ 1/4[max{∥Re(T)+Im(T)∥4,∥Re(T)-Im(T)∥4}+3∥Re(T)+Im(T)∥2∥Re(T)-Im(T)∥2]1/2, where Re(T)=(T+T*)/2 and Im(T)=(T-T*)/2i are the real and imaginary parts of T, respectively. Finally, the upper bound of the numerical radius of adjointable 2 × 2 matrices on Hilbert C*-module is obtained by using Buzano’s inequality. Moreover, when the Hilbert C*-module degenerates into a Hilbert space and the parameters take special values, the conclusions of this paper improve the results on the upper bounds of the numerical radius of 2×2 bounded linear operator matrices in Hilbert spaces obtained by Bani-Domi W and Kittaneh F. |
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