A+ CATEGORY SCIENTIFIC UNIT

A remark on the distortion of twisted sums

Jesús Suárez Colloquium Mathematicum MSC: Primary 46B03; Secondary 46B20, 46B06 DOI: 10.4064/cm9379-10-2024 Published online: 27 November 2024

Abstract

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.

Authors

  • Jesús SuárezDepartamento de Matemáticas
    Universidad de Extremadura
    06011 Badajoz, Spain
    e-mail

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