A remark on the distortion of twisted sums

Odell and Schlumprecht solved the distortion problem by proving that the classical sequence spaces $\ell _p$ for $1 \lt p \lt \infty $ admit an inevitable biorthogonal system. In particular, these spaces are arbitrarily distortable. Later, Maurey extended the result to asymptotic $\ell _p$-spaces, while Tomczak-Jaegermann did likewise for the Schatten classes. We observe that the Kalton–Peck spaces $Z_p$ for $1 \lt p \lt \infty $ admit an inevitable biorthogonal system. Therefore, we may add this classical family to the list of arbitrarily distortable spaces.