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arXiv · 1102.0137

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

Detelin Dosev·William B. Johnson·Gideon Schechtman
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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.

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Detelin Dosev, William B. Johnson, Gideon Schechtman. 2011-02-01. Commutators on $L_p$, $1\le p<\infty$. https://arxiv.org/abs/1102.0137

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