Commutators on 𝐿_{𝑝}, 1≤𝑝<∞

Dosev, Detelin; Johnson, William; Schechtman, Gideon

doi:10.1090/S0894-0347-2012-00748-6

Commutators on $L_p$, $1\leq p <\infty$
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by Detelin Dosev, William B. Johnson and Gideon Schechtman

J. Amer. Math. Soc. 26 (2013), 101-127

DOI: https://doi.org/10.1090/S0894-0347-2012-00748-6

Published electronically: August 21, 2012

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Abstract:

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

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