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Notes on matrix inequalities and positive multilinear mappings | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 10، دوره 17، شماره 7، مهر 2026، صفحه 113-121 اصل مقاله (368.19 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.30483.4412 | ||
| نویسنده | ||
| Leila Nasiri* | ||
| Department Mathematics, Lorestan University, Iran | ||
| تاریخ دریافت: 08 اردیبهشت 1402، تاریخ پذیرش: 01 آبان 1403 | ||
| چکیده | ||
| In this paper, our aim is to prove some matrix inequalities involving arbitrary matrix means and positive multilinear mappings. For example, it is shown that for Hermitian matrices $A_{i}, B_{i}$ such that $0 < m \leq A_{i},B_{i} \leq M \,\,(i=1,\cdots, k),$ \begin{align*} \Phi^{2} (A_{1} \sigma_{1} B_{1}, \cdots ,A_{k} \sigma_{1} B_{k} ) \leq \left(K(u^{k})\right)^{2} \Phi^{2} (A_{1} \sigma_{2} B_{1}, \cdots ,A_{k} \sigma_{2} B_{k} ), \end{align*} where $\sigma_{1}$ and $ \sigma_{2} $ are two arbitrary matrix means between the arithmetic and harmonic means, $\Phi:\mathscr{M}_n^k(\mathbb{C}) \rightarrow \mathscr{M}_l(\mathbb{C})$ is a positive unital multilinear mapping, $u=\frac{M}{m} $ and $K(u)=\frac{(1+u)^{2}}{4 u}$. We also give the obtained results for the adjoint and the dual of an arbitrary matrix mean. | ||
| کلیدواژهها | ||
| Matrix means؛ Kantorovich's constant؛ Positive multilinear mapping؛ Dual؛ Adjoint | ||
| مراجع | ||
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