Commutators on $L_p$, $1\le p<\infty$

Detelin Dosev, William B. Johnson, Gideon Schechtman

Published 2011-02-01Version 1

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.