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A remark on the distortion of twisted sums

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arXiv:2403.18037v1 Announce Type: new
Abstract: Odell and Schlumprecht solved the distortion problem by proving that the classic sequence spaces $\ell_p$ for $1

<\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

<\infty$ admit an inevitable biorthogonal system. Therefore, we may add this classic family to the list of arbitrarily distortable spaces.

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