Thomas Schlumprecht

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math.FA2025

Lower-Order Refinements of Greedy Approximation

Kevin Beanland, Hung Viet Chu, Thomas Schlumprecht +1

For two countable ordinals $I^\pm$ and $I^^{2}$ , a basis of a Banach space $X$ is said to be $(I^\pm, I^^{2})$ -quasi-greedy if it is 1) quasi-greedy, 2) $S_{I^} \pm$ -unconditional but not $\…

math.FA2025

On the uniform continuity of homeomorphisms between the spheres of $ℓ_{\infty}^{k}$ and $ℓ_{1}^{k}$

Bruno de MendonÃ§a Braga, Chris Gartland, Gilles Lancien +3

We consider the problem of whether there is a sequence of homeomorphisms $(F_{k})_{k}$ between the unit spheres of the $k$ -dimensional Banach spaces $ℓ_{\infty}^{k}$ and $ℓ_{1}^{k}$ whic…

math.FA2024

Higher Order Tsirelson Spaces and their Modified Versions are Isomorphic

Hung Viet Chu, Thomas Schlumprecht

We prove that for every countable ordinal $I^¾$ , the Tsirelson's space $T_{I^} ¾$ of order $I^¾$ , is naturally, i.e., via the identity, $3$ -isomorphc to its modified version. For the fir…

Lower-Order Refinements of Greedy Approximation

On the uniform continuity of homeomorphisms between the spheres of ℓ∞k​ and ℓ1k​

Higher Order Tsirelson Spaces and their Modified Versions are Isomorphic

On the uniform continuity of homeomorphisms between the spheres of $ℓ_{\infty}^{k}$ and $ℓ_{1}^{k}$