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Inequalities for Unitarily Invariant Norms
SIAM Journal on Matrix Analysis and Applications, 1998Let \(A,B,X\) be complex matrices with \(A,B\) positive semidefinite. The author proves the following generalization of the arithmetic-mean inequality due to \textit{R. Bhatia} and \textit{C. Davis} [ibid. 14, No. 1, 132-136 (1993; Zbl 0767.15012]: \[ (2+t)\| A^rXB^{2-r}+A^{2-r}XB^r\| \leq 2\| A^2X+tAXB+XB^2\| \] for arbitrary unitarily invariant norm \
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Hölder-type inequalities involving unitarily invariant norms
Positivity, 2011The author proves that, if \(A, B\) and \(X\) are operators acting on a complex Hilbert space, then \[ \left| \left| \left| {} \left| A^{\ast }XB\right|^{r} \right| \right| \right| ^{2}\leq \left| \left| \left| \left( A^{\ast }\left| X^{\ast} \right| A\right) ^{\frac{ pr}{2}} \right| \right| \right| ^{\frac{1}{p}} \left| \left| \left| \left( B^{\ast ...
Hussien Albadawi
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Unitarily invariant generalized matrix norms and hadamard products
Linear and Multilinear Algebra, 1984Let ‖ · ‖ be a unitarily invariant generalized matrix norm on Mn (C) the space of n-square complex matrices. Theorems are developed relating the Hadamard product (entrywise product) of two matrices A,BeMn (C) to the singular values of A and B. We conjecture that for any such norm. where A · B denotes the Hadamard product. For p ⩾ 1,1 ⩽ k ⩽ n, let where
Marvin Marcus, Kent Kidman, Markus Sandy
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SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS
The Quarterly Journal of Mathematics, 1960openaire +4 more sources
Unitarily Invariant Operator Norms
Canadian Journal of Mathematics, 19831.1. Over the past 15 years there has grown up quite an extensive theory of operator norms related to the numerical radius1of a Hilbert space operator T. Among the many interesting developments, we may mention:(a) C. Berger's proof of the “power inequality”2(b) R. Bouldin's result that3for any isometry V commuting with T;(c) the unification by B.
Fong, C.-K., Holbrook, J. A. R.
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Unitarily invariant norm submultiplicativity
Linear and Multilinear Algebra, 1992In this paper, we view rules for multiplying matrices (such as the Hadamard product, usual product and Kronecker product) as combinatorial objects. Our purpose is to determine conditions on these objects that imply submultiplicativity with respect to the spectral norm and certain of the unitarily invariant norms.
Charles R. Johnson, Peter Nylen
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A note on unitarily invariant matrix norms
Linear Algebra and its Applications, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ding, Wenxuan, Li, Chi-Kwong, Li, Yuqiao
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Unitarily invariant norm inequalities for positive semidefinite matrices
Linear Algebra and its Applications, 2022Let \(M_n(\mathbb{C})\) denote the space of all \(n\times n\) complex matrices. \textit{F. Kittaneh} [J. Funct. Anal. 250, No. 1, 132--143 (2007; Zbl 1131.47009)] proved that if \(A, B, X \in M_n(\mathbb{C})\) such that \(A, B\) are positive semidefinite, then \[ \|| AX-XB |\| \le \Vert X\Vert~\|| A \oplus B |\|, \] where \(\|| \cdot |\|\) denotes the ...
Al-Natoor, Ahmad +2 more
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Unitarily invariant norms on finite von Neumann algebras
Acta Scientiarum Mathematicarum, 2023The authors generalize the celebrated theorem of \textit{J. von Neumann} [Mitt. Forsch.-Inst. Math. Mech. Univ. Tomsk 1, 286--299 (1937; Zbl 0017.09802)] on unitarily invariant norms on \(n\times n\) matrices to the context of finite von Neumann algebras \(\mathcal{R}\). A norm \(\alpha\) on a unital \(C^*\)-algebra \(\mathcal{A}\) is called normalized
Haihui Fan, Don Hadwin
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