Impressions of convexity - An illustration for commutator bounds

Details Impressions of convexity - An illustration for commutator bounds Impressions of convexity - An illustration for commutator bounds

2010-04-15

arxiv.org/abs/1004.2700v1

Lin. Alg. Appl. 433(11-12), 1726-1759 (2010)

Mathematics

Functional Analysis

32 pages, 88 pictures

Scientific paper

We determine the sharpest constant $C_{p,q,r}$ such that for all complex
matrices $X$ and $Y$, and for Schatten $p$-, $q$- and $r$-norms the inequality
$$ \|XY-YX\|_p\leq C_{p,q,r}\|X\|_q\|Y\|_r $$ is valid. The main theoretical
tool in our investigations is complex interpolation theory.

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