Jensen matrix inequalities and direct sums |
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| Authors: | Jean-Christophe Bourin Omar Hirzallah Fuad Kittaneh |
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| Affiliation: | 1. Laboratoire de Mathématiques , Université de Franche-Comté , Besan?on, France jcbourin@univ-fcomte.fr;3. Department of Mathematics , Hashemite University , Zarqa, Jordan;4. Department of Mathematics , University of Jordan , Amman, Jordan |
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| Abstract: | Let A, X and Y be n-by-n complex matrices such that A is positive semi-definite and X, Y are contractions. We prove that if f is an increasing convex function on [0, ∞) such that f(0) ≤ 0, then the eigenvalues of f(|X*AY|) are dominated by those of X*f(A)X⊕Y* f(A)Y. Several related results are considered. |
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| Keywords: | eigenvalue unitarily invariant norm Jensen inequality direct sum |
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