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

preprint2011arXivOpen access

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

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

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Commutators on LpL_pLp​, 1≤p<∞1\le p<\infty1≤p<∞

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