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arXiv · 2112.09602

On uniqueness and plentitude of subsymmetric sequences

Peter G. Casazza·Stephen J. Dilworth·Denka Kutzarova·Pavlos Motakis
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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 subsymmetric 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 $\ell_p$ or $c_0$.

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Peter G. Casazza, Stephen J. Dilworth, Denka Kutzarova, Pavlos Motakis. 2021-12-17. On uniqueness and plentitude of subsymmetric sequences. https://arxiv.org/abs/2112.09602

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