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Search name	Searched On	Run search
[in Journal: Journal of Algebra and Its Applications] AND [Keyword: Matrix] (3)	27 Mar 2025	Run
[in Journal: International Journal of Mathematics] AND [Keyword: Matrix] (1)	27 Mar 2025	Run
[in Journal: Journal of Advanced Dielectrics] AND [Keyword: Matrix] (2)	27 Mar 2025	Run
[in Journal: Biomedical Engineering: Applications, Basis and Communications] AND [K... (1)	27 Mar 2025	Run
[in Journal: Reviews in Mathematical Physics] AND [Keyword: S-wave] (1)	27 Mar 2025	Run

articleNo Access
NORM AND ANTI-NORM INEQUALITIES FOR POSITIVE SEMI-DEFINITE MATRICES
- JEAN-CHRISTOPHE BOURIN and
- FUMIO HIAI
International Journal of Mathematics01 Aug 2011
Preview Abstract
Some subadditivity results involving symmetric (unitarily invariant) norms are obtained. For instance, if is a polynomial of degree m with non-negative coefficients, then, for all positive operators A, B and all symmetric norms,
To give parallel superadditivity results, we investigate anti-norms, a class of functionals containing the Schatten q-norms for q ∈ (0, 1] and q < 0. The results are extensions of the Minkowski determinantal inequality. A few estimates for block-matrices are derived. For instance, let f : [0, ∞) → [0, ∞) be concave and p ∈(1, ∞). If f^p(t) is superadditive, then for all positive m × m matrix A = [a_ij]. Furthermore, for the normalized trace τ, we consider functions φ(t) and f(t) for which the functional A ↦ φ ◦ τ ◦ f(A) is convex or concave, and obtain a simple analytic criterion.

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