On uniqueness and plentitude of subsymmetric sequences

Peter G. Casazza, Stephen J. Dilworth, Denka Kutzarova, Pavlos Motakis

Research output: Contribution to journalArticlepeer-review

Abstract

We explore the diversity of subsymmetric basic sequences in spaces with a subsymmetric basis. We prove that the subsymmetrization Su(T*) of Tsirelson’s original Banach space provides the first known example of a space with a unique subsymmetric basic sequence that is additionally non-symmetric. Contrastingly, we provide a criterion for a space with a sub-symmetric basis to contain a continuum of nonequivalent subsymmetric basic sequences and apply it to Su(T*)*. Finally, we provide a criterion for a subsymmetric sequence to be equivalent to the unit vector basis of some ℓp or c 0.

Original languageEnglish (US)
JournalIsrael Journal of Mathematics
DOIs
StateAccepted/In press - 2023

ASJC Scopus subject areas

  • General Mathematics

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