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Mathematics > Functional Analysis

Title: A remark on the distortion of twisted sums

Abstract: Odell and Schlumprecht solved the distortion problem by proving that the classic sequence spaces $\ell_p$ for $1<p<\infty$ 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 $1<p<\infty$ admit an inevitable biorthogonal system. Therefore, we may add this classic family to the list of arbitrarily distortable spaces.
Subjects: Functional Analysis (math.FA)
MSC classes: 46B03, 46B20, 46B06
Cite as: arXiv:2403.18037 [math.FA]
  (or arXiv:2403.18037v1 [math.FA] for this version)

Submission history

From: Jesús Suárez [view email]
[v1] Tue, 26 Mar 2024 18:46:56 GMT (12kb)

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