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Sheikhhosseini, Alemeh. (1402). Schur multiplier operator and matrix inequalities. , 13(1), 383-390. doi: 10.22103/jmmr.2023.21383.1434
Alemeh Sheikhhosseini. "Schur multiplier operator and matrix inequalities". , 13, 1, 1402, 383-390. doi: 10.22103/jmmr.2023.21383.1434
Sheikhhosseini, Alemeh. (1402). 'Schur multiplier operator and matrix inequalities', , 13(1), pp. 383-390. doi: 10.22103/jmmr.2023.21383.1434
Sheikhhosseini, Alemeh. Schur multiplier operator and matrix inequalities. , 1402; 13(1): 383-390. doi: 10.22103/jmmr.2023.21383.1434

Schur multiplier operator and matrix inequalities

Journal of Mahani Mathematical Research
دوره 13، شماره 1 - شماره پیاپی 26، بهمن 2023، صفحه 383-390    اصل مقاله (474.67 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22103/jmmr.2023.21383.1434
نویسنده
Alemeh Sheikhhosseini*
Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran.
چکیده
In this note we obtain a reverse version of the Haagerup Theorem. In particular, if $ A \in \mathbb{M}_{n}$ has a $ 2\times2- $ principal submatrix as $ \left[ \begin{array}{cc}
1& \alpha \\
\beta & 1\\
\end{array}
\right]$ with $ \beta \neq \bar{\alpha}, $ then $ \Vert S_{A} \Vert > 1$ where the operator $ S_{A}:\mathbb{M}_{n}\longrightarrow \mathbb{M}_{n} $ is defined by $S_{A}(B) := A \circ B $ where $ "\circ " $ stands for Schur product.
کلیدواژه‌ها
Inequalities؛ Schur multiplier operator؛ spectral norm؛ numerical radius
مراجع
[1] Aghamollaei, Gh., & Sheikhhosseini, A. (2015). Some numerical radius inequalities with positive definite functions. Bulletin of the Iranian Mathematical Society, 41, 889-900.

[2] Ando, T., & Okubo, K. (1991). Induced norms of the Schur multiplication operator. Linear Algebra and its Applications, 147, 181-199.

[3] Bakherad, M., Krnic, M., & Sal Moslehian, M. (2016). Reverse Young-type inequalities for matrices and operators. Rocky Mountain Journal of Mathematics, 46, 1089-1104.

[4] Bhatia, R. (2007). Positive Definite Matrices, Princeton University Press.

[5] Khosravi, M. & Sheikhhosseini, A. (2015). Shur multiplier norm of product of matrices. Wavelets and Linear Algebra, 2, 49-54.

[6] Sababheh, M. (2018). Heinz-type numerical radii inequalities. Linear and Multilinear Algebra, 67, 953-964.

[7] Salemi A. & Sheikhhosseini, A. (2013). Matrix Young numerical radius inequalities. Mathematical Inequalities and Applications, 16, 783-791.

[8] Salemi, A. & Sheikhhosseini, A. (2014). On reversing of the modified Young inequality. Annals of Functional Analysis, 5, 69-75.

[9] Sheikhhosseini, A. (2017). An AM-GM mean inequality related to numerical redius of matrices. Konuralp Journal of Mathematics, 5, 116-122.

[10] Xu, K. Pedrycz, Z., W., Li, Z. & Nie, W. (2019). High-accuracy signal subspace separation algorithm based on Gaussian kernel soft partition, IEEE Transactions on Industrial Electronics, 66(1), 491-499.

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