The Kalton centralizer on 𝐿_{𝑝}[0,1] is not strictly singular

de la Fuente, Jesús

doi:10.1090/S0002-9939-2013-11599-6

The Kalton centralizer on $L_p[0,1]$ is not strictly singular
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by Jesús Suárez de la Fuente PDF

Proc. Amer. Math. Soc. 141 (2013), 3447-3451 Request permission

Abstract:

We prove that the Kalton centralizer on $L_p[0,1]$, for $0<p<\infty$, is not strictly singular: in all cases there is a Hilbert subspace on which it is trivial. Moreover, for $0<p<2$ there are copies of $\ell _q$, with $p<q<2$, on which it becomes trivial. This is in contrast to the situation for $\ell _p$ spaces, in which the Kalton-Peck centralizer is strictly singular.

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