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 σ1 and σ2 are non-zero connections, and if A, B, and C belong to Sα, such that R (Aσ1(Bσ2C)) ≤ cos4(α) R ((Aσ1B)σ2(Aσ1C)) ,then R (Aσ∗ 1 (Bσ∗ 2 C)) ≥ cos4(α) R ((Aσ∗ 1 B)σ∗ 2 (Aσ∗ 1 C)) .
Malekinejad,S. and Mohammadzadehkan,H. (2023). ADJOINTATIONS OF OPERATOR INEQUALITIES FOR SECTOR MATRICES. Mathematical Analysis and Convex Optimization, 4(2), 51-59. doi: 10.22034/maco.4.2.6
MLA
Malekinejad,S. , and Mohammadzadehkan,H. . "ADJOINTATIONS OF OPERATOR INEQUALITIES FOR SECTOR MATRICES", Mathematical Analysis and Convex Optimization, 4, 2, 2023, 51-59. doi: 10.22034/maco.4.2.6
HARVARD
Malekinejad S., Mohammadzadehkan H. (2023). 'ADJOINTATIONS OF OPERATOR INEQUALITIES FOR SECTOR MATRICES', Mathematical Analysis and Convex Optimization, 4(2), pp. 51-59. doi: 10.22034/maco.4.2.6
CHICAGO
S. Malekinejad and H. Mohammadzadehkan, "ADJOINTATIONS OF OPERATOR INEQUALITIES FOR SECTOR MATRICES," Mathematical Analysis and Convex Optimization, 4 2 (2023): 51-59, doi: 10.22034/maco.4.2.6
VANCOUVER
Malekinejad S., Mohammadzadehkan H. ADJOINTATIONS OF OPERATOR INEQUALITIES FOR SECTOR MATRICES. MACO, 2023; 4(2): 51-59. doi: 10.22034/maco.4.2.6
Mathematical Analysis and Convex Optimization