This is an announcement for the paper "A quantitative version of the commutator theorem for zero trace matrices" by William B. Johnson, Naratuka Ozawa, and Gideon Schechtman.

Abstract: 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.

Archive classification: math.FA

Mathematics Subject Classification: 47B47, 15A60

Submitted from: gideon@weizmann.ac.il

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1202.0986

or

http://arXiv.org/abs/1202.0986