Thomas Schlumprecht

activity

20232026

collaborators

8 papers

math.FA2026

On complementation and $L$ -embedding of Lipschitz-free spaces in their biduals

Bruno M. Braga, Chris Gartland, Gilles Lancien +3

A closed subspace $E$ of a Banach space $F$ is \emph{ $L$ -embedded in $F$ } if there is a projection $P : F \to E$ such that $∥ x ∥ = ∥ P x ∥ + ∥ x - P x ∥$ for all $x \in F$ . We show that…

math.FA2026

On the $L$ -embeddability of Lipschitz-free spaces in their biduals

Bruno de Mendonça Braga, Chris Gartland, Gilles Lancien +3

A Banach space $X$ is $L$ -embedded in its bidual if there is a projection $P : X^{**} \to X$ such that $∥ x ∥ = ∥ P x ∥ + ∥ x - P x ∥$ for all $x \in X^{**}$ . We show that, as long as $X…

math.FA2026

Expanders prevent Property (H)

Bruno de Mendonç Braga, Chris Gartland, Gilles Lancien +3

We show that if a sequence of expander graphs equi-coarsely embeds into a Banach space, then this Banach space fails Kasparov and Yu's Property (H). Consequently, no Banach space w…

math.FA2025

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

Bruno de Mendonça 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.FA2025

Lower-Order Refinements of Greedy Approximation

Kevin Beanland, Hung Viet Chu, Thomas Schlumprecht +1

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

math.FA2024

Higher Order Tsirelson Spaces and their Modified Versions are Isomorphic

Hung Viet Chu, Thomas Schlumprecht

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

math.FA2023

Multipliers on bi-parameter Haar system Hardy spaces

Richard Lechner, Pavlos Motakis, Paul F. X. Müller +1

Let $(h_{I})$ denote the standard Haar system on $[0, 1]$ , indexed by $I \in D$ , the set of dyadic intervals and $h_{I} \otimes h_{J}$ denote the tensor product $(s,t)\mapsto h_I(s…

math.FA2023

Transportation cost spaces and their embeddings into $L_{1}$ , a Survey

Thomas Schlumprecht

These notes present a basic survey on Transportation cost spaces (aka Lipschitzfree spaces, Wasserstein spaces) and their bi-Lipschitz and linear embeddings into $L_{1}$ spaces. To m…

On complementation and L-embedding of Lipschitz-free spaces in their biduals

On the L-embeddability of Lipschitz-free spaces in their biduals

Expanders prevent Property (H)

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

Lower-Order Refinements of Greedy Approximation

Higher Order Tsirelson Spaces and their Modified Versions are Isomorphic

Multipliers on bi-parameter Haar system Hardy spaces

Transportation cost spaces and their embeddings into L1​, a Survey

On complementation and $L$ -embedding of Lipschitz-free spaces in their biduals

On the $L$ -embeddability of Lipschitz-free spaces in their biduals

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

Transportation cost spaces and their embeddings into $L_{1}$ , a Survey