Subadditivity of eigenvalue sums
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Abstract:
Let $f(t)$ be a nonnegative concave function on $0 \leq t <\infty$ with $f(0)=0$, and let $X, Y$ be $n\times n$ matrices. Then it is known that $\Vert f(|X+Y|)\Vert _1\leq \Vert f(|X|)\Vert _1 +\Vert f(|Y|)\Vert _1$, where $\Vert \cdot \Vert _1$ is the trace norm. We extend this result to all unitarily invariant norms and prove some inequalities of eigenvalue sums.References
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Additional Information
- Mitsuru Uchiyama
- Affiliation: Department of Mathematics, Fukuoka University of Education, Munakata, Fukuoka, 811-4192, Japan
- MR Author ID: 198919
- Email: uchiyama@fukuoka-edu.ac.jp
- Received by editor(s): October 23, 2004
- Received by editor(s) in revised form: December 11, 2004
- Published electronically: October 7, 2005
- Communicated by: Joseph A. Ball
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 1405-1412
- MSC (2000): Primary 47A30, 15A42; Secondary 47A75
- DOI: https://doi.org/10.1090/S0002-9939-05-08116-5
- MathSciNet review: 2199187