R. Haller

activity

20132026

most citedStability of average roughness, octahedrality, and strong diameter 2 properties of Banach spaces with respect to absolute sums

10 citations · 24 across the 14 of their papers we have counts for

collaborators

22 papers

math.FA2026

Isometric copies of $ℓ_{\infty}^{n}$ in Lipschitz-free spaces over finite metric spaces

Rainis Haller

For every $n \in N$ , we construct a finite metric subspace $M_{n}$ of $ℓ_{\infty}^{n}$ such that the Lipschitz-free space $F (M_{n})$ contains a linear isometric copy of $…

math.FA2026

Weak stability and binary convex combinations of slices

Rainis Haller

We study weak openness and related geometric properties of convex combinations of slices of the unit balls of Banach spaces. We prove that, for every $m \geq 2$ , properties $\mathrm…

math.FA2026

Plasticity of the unit ball of the real Banach space $ℓ_{\infty}$

Rainis Haller, Nikita Leo

We prove that the closed unit ball of the real Banach space $ℓ_{\infty}$ is plastic, that is, every non-expansive bijection from the unit ball onto itself is an isometry. The main…

math.FA2026

A counterexample for the Daugavet index of thickness in $ℓ_{1}$ -sums

Rainis Haller, Andre Ostrak

We give a negative answer to a question of Haller-Langemets-Lima-Nadel-Rueda Zoca asking whether, for all Banach spaces $X$ and $Y$ , the Daugavet index of thickness satisfies \[ T(…

math.FA2025

Norm-one points in convex combinations of relatively weakly open subsets of the unit ball in the spaces $L_{1} (μ, X)$

Rainis Haller, Paavo Kuuseok, Märt Põldvere

In a paper published in 2020 in Studia Mathematica, Abrahamsen et al. proved that in the real space $L_{1} (μ)$ , where $μ$ is a non-zero $σ$ -finite (countably additive non-negative) m…

math.FA2025

The local diameter two property and the diameter two property in spaces of Lipschitz functions

Rainis Haller, Jaan Kristjan Kaasik, Andre Ostrak

We separate the local diameter two property from the diameter two property and their weak-star counterparts from each other in spaces of Lipschitz functions. We characterise the $w…

math.FA2024

Separating diameter two properties from their weak-star counterparts in spaces of Lipschitz functions

Rainis Haller, Jaan Kristjan Kaasik, Andre Ostrak

We address some open problems concerning Banach spaces of real-valued Lipschitz functions. Specifically, we prove that the diameter two properties differ from their weak-star count…

math.FA2023

Unconditional bases and Daugavet renormings

Rainis Haller, Johann Langemets, Yoël Perreau +1

We introduce a new diametral notion for points of the unit sphere of Banach spaces, that naturally complements the notion of Delta-points, but is weaker than the notion of Daugavet…

math.FA2022★ 1 cited

Diameter two properties for spaces of Lipschitz functions

Rainis Haller, Andre Ostrak, Märt Põldvere

We solve some open problems regarding diameter two properties within the class of Banach spaces of real-valued Lipschitz functions by using the de Leeuw transform. Namely, we show…

math.FA2022

The Lipschitz-free space over length space is locally almost square but never almost square

Rainis Haller, Jaan Kristjan Kaasik, Andre Ostrak

We prove that the Lipschitz-free space over a metric space M is locally almost square whenever M is a length space. Consequently, the Lipschitz-free space is locally almost square…

math.FA2021

Two new examples of Banach spaces with a plastic unit ball

Rainis Haller, Nikita Leo, Olesia Zavarzina

We prove that Banach spaces $ℓ_{1} \oplus_{2} R$ and $X \oplus_{\infty} Y$ , with strictly convex $X$ and $Y$ , have plastic unit balls (we call a metric space plastic if every no…

math.FA2020

On Daugavet indices of thickness

Rainis Haller, Johann Langemets, Vegard Lima +2

Inspired by R. Whitley's thickness index the last named author recently introduced the Daugavet index of thickness of Banach spaces. We continue the investigation of the behavior o…

math.FA2020★ 9 cited

Daugavet- and Delta-points in absolute sums of Banach spaces

Rainis Haller, Katriin Pirk, Triinu Veeorg

A Daugavet-point (resp.~ $Δ$ -point) of a Banach space is a norm one element $x$ for which every point in the unit ball (resp.~element $x$ itself) is in the closed convex hull of uni…

math.FA2018

Delta- and Daugavet-points in Banach spaces

Trond Arnold Abrahamsen, Rainis Haller, Vegard Lima +1

A $Δ$ -point $x$ of a Banach space is a norm one element that is arbitrarily close to convex combinations of elements in the unit ball that are almost at distance $2$ from $x$ . If,…

math.FA2018

Banach spaces where convex combinations of relatively weakly open subsets of the unit ball are relatively weakly open

Trond Arnold Abrahamsen, Julio Becerra Guerrero, Rainis Haller +2

We introduce and study Banach spaces which have property CWO, i.e., every finite convex combination of relatively weakly open subsets of their unit ball is open in the relative wea…

math.FA2018

Symmetric strong diameter two property

Rainis Haller, Johann Langemets, Vegard Lima +1

We study Banach spaces with the property that, given a finite number of slices of the unit ball, there exists a direction such that all these slices contain a line segment of lengt…

math.FA2017★ 4 cited

On convex combinations of slices of the unit ball in Banach spaces

Rainis Haller, Paavo Kuuseok, Märt Põldvere

We prove that the following three properties for a Banach space are all different from each other: every finite convex combination of slices of the unit ball is (1) relatively weak…

math.FA2017★ 10 cited

Stability of average roughness, octahedrality, and strong diameter 2 properties of Banach spaces with respect to absolute sums

Rainis Haller, Johann Langemets, Rihhard Nadel

We prove that, if Banach spaces $X$ and $Y$ are $δ$ -average rough, then their direct sum with respect to an absolute norm $N$ is $δ / N (1, 1)$ -average rough. In particular, for octahe…

math.FA2016

Rough norms in spaces of operators

Rainis Haller, Johann Langemets, Märt Põldvere

We investigate sufficient and necessary conditions for the space of bounded linear operators between two Banach spaces to be rough or average rough. Our main result is that $\mathc…

math.FA2016

Diametral strong diameter two property of Banach spaces is stable under direct sums with 1-norm

Rainis Haller, Katriin Pirk, Märt Põldvere

We prove that the diametral strong diameter 2 property of a Banach space (meaning that, in convex combinations of relatively weakly open subsets of its unit ball, every point has a…

math.FA2014

Geometry of Banach spaces with an octahedral norm

Rainis Haller, Johann Langemets

We discuss the geometry of Banach spaces whose norm is octahedral or, more generally, locally or weakly octahedral. Our main results characterize these spaces in terms of covering…

math.FA2013

On duality of diameter 2 properties

Rainis Haller, Johann Langemets, Märt Põldvere

It is known that a Banach space has the strong diameter 2 property (i.e. every convex combination of slices of the unit ball has diameter 2) if and only if the norm on its dual spa…

Isometric copies of ℓ∞n​ in Lipschitz-free spaces over finite metric spaces

Weak stability and binary convex combinations of slices

Plasticity of the unit ball of the real Banach space ℓ∞​

A counterexample for the Daugavet index of thickness in ℓ1​-sums

Norm-one points in convex combinations of relatively weakly open subsets of the unit ball in the spaces L1​(μ,X)

The local diameter two property and the diameter two property in spaces of Lipschitz functions

Separating diameter two properties from their weak-star counterparts in spaces of Lipschitz functions

Unconditional bases and Daugavet renormings

Diameter two properties for spaces of Lipschitz functions

The Lipschitz-free space over length space is locally almost square but never almost square

Two new examples of Banach spaces with a plastic unit ball

On Daugavet indices of thickness

Daugavet- and Delta-points in absolute sums of Banach spaces

Delta- and Daugavet-points in Banach spaces

Banach spaces where convex combinations of relatively weakly open subsets of the unit ball are relatively weakly open

Symmetric strong diameter two property

On convex combinations of slices of the unit ball in Banach spaces

Stability of average roughness, octahedrality, and strong diameter 2 properties of Banach spaces with respect to absolute sums

Rough norms in spaces of operators

Diametral strong diameter two property of Banach spaces is stable under direct sums with 1-norm

Geometry of Banach spaces with an octahedral norm

On duality of diameter 2 properties

Isometric copies of $ℓ_{\infty}^{n}$ in Lipschitz-free spaces over finite metric spaces

Plasticity of the unit ball of the real Banach space $ℓ_{\infty}$

A counterexample for the Daugavet index of thickness in $ℓ_{1}$ -sums

Norm-one points in convex combinations of relatively weakly open subsets of the unit ball in the spaces $L_{1} (μ, X)$