Volume 4, Issue 2 (12-2023)                   MACO 2023, 4(2): 51-59 | Back to browse issues page

XML Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Malekinejad S, Mohammadzadehkan H. Adjointations of Operator Inequalities for Sector Matrices. MACO 2023; 4 (2) :51-59
URL: http://maco.lu.ac.ir/article-1-159-en.html
Abstract:   (191 Views)
In this paper, we first extend the well-known inequalities to the case of sector matrices. We also explore the adjointness of operator inequalities with binary operations for sector matrices. As a result of our exploration, we establish four distinct inequalities: a matrix inequality, a unitarily invariant norm inequality, a singular value inequality, and a determinant inequality. For example, we demonstrate that if $sigma_{1}$ and $ sigma_{2} $ are non-zero connections, and if $A$, $B$, and $C$ belong to $mathcal{S}_{alpha}$,  such that
	begin{equation*}
	mathcal{R}left(A  sigma_{1}  (B  sigma_{2}  C)right) leq cos^{4}(alpha)  mathcal{R}left((A  sigma_{1}  B)  sigma_{2}  (A  sigma_{1}  C)right),
	end{equation*}
	then
	begin{equation*}
	mathcal{R}left(A  sigma_{1}^* (B  sigma_{2}^*  C)right)geq cos^{4}(alpha)  mathcal{R}left((A sigma_{1}^*   B)  sigma_{2}^*  (A  sigma_{1}^*  C)right).
	end{equation*}
Full-Text [PDF 120 kb]   (131 Downloads)    
Type of Study: Research Article | Subject: Mathematical Analysis
Published: 2024/10/11

Send email to the article author


Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.