This is an announcement for the paper "Commutators on $L_p$, $1\le p<\infty$" by Detelin Dosev, William B. Johnson, and Gideon Schechtman.

Abstract: The operators on $\LP=L_p[0,1]$, $1\leq p<\infty$, which are not commutators are those of the form $\lambda I + S$ where $\lambda\neq 0$ and $S$ belongs to the largest ideal in $\opLP$. The proof involves new structural results for operators on $\LP$ which are of independent interest.

Archive classification: math.FA

Mathematics Subject Classification: 47B47, 46E30

Submitted from: gideon@weizmann.ac.il

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

http://front.math.ucdavis.edu/1102.0137

or

http://arXiv.org/abs/1102.0137