T. Schlumprecht

activity

19922023

most citedCoefficient Quantization for Frames in Banach Spaces

51 citations · 253 across the 61 of their papers we have counts for

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49 papers · 1 filter

math.FA2023

On stability of metric spaces and Kalton's property $Q$

F. Baudier, Th. Schlumprecht, A. Zsák

The first named author introduced the notion of upper stability for metric spaces as a relaxation of stability. The motivation was a search for a new invariant to distinguish the c…

math.FA2021

The space $L_{1} (L_{p})$ is primary for $1 < p < \infty$

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

The classical Banach space $L_{1} (L_{p})$ consists of measurable scalar functions $f$ on the unit square for which $$\|f\| = \int_0^1\Big(\int_0^1 |f(x,y)|^p dy\Big)^{1/p}dx < \infty.$…

math.FA2020

The cardinality of the sublattice of closed ideals of operators between certain classical sequence spaces

Daniel Freeman, Thomas Schlumprecht, Andras Zsak

Theorem A and Theorem B of [1] state that for $1 < p < \infty$ the lattice of closed ideals of $L (ℓ_{p}, c_{0})$ , $L (ℓ_{p}, ℓ_{\infty})$ and of $\mathcal{L}(\ell_1,\…

math.FA2020★ 2 cited

Banach spaces for which the space of operators has $2^{c}$ closed ideals

Daniel Freeman, Thomas Schlumprecht, Andras Zsak

We formulate general conditions which imply that $L (X, Y)$ , the space of operators from a Banach space $X$ to a Banach space $Y$ , has $2^{c}$ closed ideals where $\mathfra…

math.FA2020

The geometry of Hamming-type metrics and their embeddings into Banach spaces

Florent P. Baudier, Gilles Lancien, Pavlos Motakis +1

Within the class of reflexive Banach spaces, we prove a metric characterization of the class of asymptotic- $c_{0}$ spaces in terms of a bi-Lipschitz invariant which involves metrics…

math.FA2019★ 1 cited

The factorization property of $ℓ^{\infty} (X_{k})$

R. Lechner, P. Motakis, P. F. X. Müller +1

In this paper we consider the following problem: Let $X_{k}$ , be a Banach space with a normalized basis $(e_{(k, j)})_{j}$ , whose biorthogonals are denoted by $(e_{(k, j)}^{*})_{j}$ , for $k\…

math.FA2018★ 8 cited

Strategically reproducible bases and the factorization property

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

We introduce the concept of strategically reproducible bases in Banach spaces and show that operators which have large diagonal with respect to strategically reproducible bases are…

math.FA2017

Generalization of a theorem of Zippin

Petr Hajek, Thomas Schlumprecht, Andras Zsak

We generalize and prove a result which was first shown by Zippin, and was explicitly formulated by Benyamini.

math.FA2017★ 24 cited

The coarse geometry of Tsirelson's space and applications

Florent Baudier, Gilles Lancien, Thomas Schlumprecht

The main result of this article is a rigidity result pertaining to the spreading model structure for Banach spaces coarsely embeddable into Tsirelson's original space $T^{*}$ . Every…

math.FA2017

Coarse embeddings into $c_{0} (Γ)$

Petr Hajek, Thomas Schlumprecht

Let $λ$ be a large enough cardinal number (assuming GCH it suffices to let $λ = ℵ_{ω}$ ). If $X$ is a Banach space with $dens (X) \geq λ$ , which admits a coarse (or uniform) emb…

math.FA2016★ 9 cited

Closed Ideals of Operators between the Classical Sequence Spaces

Dan Freeman, Thomas Schlumprecht, Andras Zsak

We prove that the spaces $L (ℓ_{p}, c_{0})$ , $L (ℓ_{p}, ℓ_{\infty})$ and $L (ℓ_{1}, ℓ_{q})$ of operators with $1 < p, q < \infty$ have continuum many cl…

math.FA2016★ 3 cited

A metric interpretation of reflexivity for Banach spaces

Pavlos Motakis, Thomas Schlumprecht

We define two metrics $d_{1, α}$ and $d_{\infty, α}$ on each Schreier family $S_{α}$ , $α < ω_{1}$ , with which we prove the following metric characterization of reflexivity of a B…

math.FA2016

On the boundedness of threshold operators in $L_{1} [0, 1]$ with respect to the Haar basis

Steven J. Dilworth, Smbat Gogyan, Denka Kutzarova +1

We prove a near-unconditionality property for the normalized Haar basis of $L_{1} [0, 1]$ .

math.FA2014★ 5 cited

The algebra of bounded linear operators on $ℓ_{p} \oplus ℓ_{q}$ has infinitely many closed ideals

Thomas Schlumprecht, András Zsák

We prove that in the reflexive range $1 < p < q < \infty$ the algebra of all bounded linear operators on $ℓ_{p} \oplus ℓ_{q}$ has infinitely many closed ideals. This solves a problem rai…

math.FA2014

On Zippin's Embedding Theorem of Banach spaces into Banach spaces with bases

Thomas Schlumprecht

We present a new proof of Zippin's Embedding Theorem, that every separable reflexive Banach space embeds into one with shrinking and boundedly complete basis, and every Banach spac…

math.FA2014★ 1 cited

The metric geometry of the Hamming cube and applications

F. Baudier, D. Freeman, Th. Schlumprecht +1

The Lipschitz geometry of segments of the infinite Hamming cube is studied. Tight estimates on the distortion necessary to embed the segments into spaces of continuous functions on…

math.FA2014

Renorming spaces with greedy bases

S. J. Dilworth, D. Kutzarova, E. Odell +2

We study the problem of improving the greedy constant or the democracy constant of a basis of a Banach space by renorming. We prove that every Banach space with a greedy basis can…

math.FA2013

The Szlenk Index of L_p(X)

Petr Hajek, Thomas Schlumprecht

We find an optimal upper bound on the values of the weak $^{*}$ -dentability index $D z (X)$ in terms of the Szlenk index $S z (X)$ of a Banach space $X$ with separable dual. Namely, if $\…

math.FA2013★ 7 cited

Equilateral sets in uniformly smooth Banach spaces

D. Freeman, E. Odell, B. Sari +1

Let $X$ be an infinite dimensional uniformly smooth Banach space. We prove that $X$ contains an infinite equilateral set. That is, there exists a constant $λ > 0$ and an infinite seq…

math.FA2012★ 3 cited

Unconditional structures of translates for $L_{p} (R^{d})$

D. Freeman, E. Odell, Th. Schlumprecht +1

We prove that a sequence $(f_{i})_{i = 1}^{\infty}$ of translates of a fixed $f \in L_{p} (R)$ cannot be an unconditional basis of $L_{p} (R)$ for any $1 \leq p < \infty$ . In contrast to this, for…

math.FA2011★ 7 cited

Subsequential minimality in Gowers and Maurey spaces

Valentin Ferenczi, Thomas Schlumprecht

We define block sequences $(x_{n})$ in every block subspace of a variant of the space of Gowers and Maurey so that the map $x_{2 n - 1} \mapsto x_{2 n}$ extends to an isomorphism. This i…

math.FA2011

On the closed subideals of $L (ℓ_{p} \oplus ℓ_{q})$

Thomas Schlumprecht

In this paper we first review the known results about the closed subideals of the space of bounded operator on $ℓ_{p} \oplus ℓ_{q}$ , $1 < p < q < \infty$ , and then construct several new…

math.FA2011★ 4 cited

Shift invariant preduals of $ℓ_{1} (Z)$

Matthew Daws, Richard Haydon, Thomas Schlumprecht +1

The Banach space $ℓ_{1} (Z)$ admits many non-isomorphic preduals, for example, $C (K)$ for any compact countable space $K$ , along with many more exotic Banach spaces. In this paper…

math.FA2009

Greedy bases for Besov spaces

S. J. Dilworth, D. Freeman, E. Odell +1

We prove thatthe Banach space $(\oplus_{n = 1}^{\infty} ℓ_{p}^{n})_{ℓ_{q}}$ , which is isomorphic to certain Besov spaces, has a greedy basis whenever $1 \leq p \leq \infty$ and $1<q<\inf…