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

Detelin Dosev, William B. Johnson, Gideon Schechtman

The operators on $\LP=L_p[0,1]$, $1\le p<\infty$, which are not commutators are those of the form $\lambda I+S$ where $\lambda \ne 0$ and $S$ belongs to the largest ideal in $\opLP$. The pro…