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We prove that the Kalton centralizer on Lp[0, 1], for 0 < p < ∞, 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 q , with p < q < 2, on which it becomes trivial. This is in contrast to the situation for p spaces, in which the Kalton-Peck centralizer is strictly singular.

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