A quantitative version of the commutator theorem for zero trace matrices

Details A quantitative version of the commutator theorem for zero trace matrices A quantitative version of the commutator theorem for zero trace matrices

2012-02-05

arxiv.org/abs/1202.0986v2

Mathematics

Functional Analysis

Scientific paper

Let $A$ be a $m\times m$ complex matrix with zero trace and let $\e>0$. Then
there are $m\times m$ matrices $B$ and $C$ such that $A=[B,C]$ and
$\|B\|\|C\|\le K_\e m^\e\|A\|$ where $K_\e$ depends only on $\e$. Moreover, the
matrix $B$ can be taken to be normal.

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