A Lieb-Thirring inequality for singular values

Details A Lieb-Thirring inequality for singular values A Lieb-Thirring inequality for singular values

2008-12-19

arxiv.org/abs/0812.3714v1

Lin. Alg. Appl. 430(11-12), 3053-3057 (2009)

Mathematics

Functional Analysis

8 pages; a Mathematica notebook is available on request

Scientific paper

Let $A$ and $B$ be positive semidefinite matrices. We investigate the
conditions under which the Lieb-Thirring inequality can be extended to singular
values. That is, for which values of $p$ does the majorisation $\sigma(B^p A^p)
\prec_w \sigma((BA)^p)$ hold, and for which values its reversed inequality
$\sigma(B^p A^p) \succ_w \sigma((BA)^p)$.

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