11 citations · 13 across the 10 of their papers we have counts for
12 papers
On the plasticity of the unit spheres of , , , and Hilbert spaces
Maksym Levchenko, Olesia Zavarzina
This paper demonstrates the expand-contract plasticity of the unit spheres of , , and . Furthermore, it establishes the strong plasticity of the unit sphe…
Plastic metric spaces and groups
Taras Banakh, Oles Mazurenko, Olesia Zavarzina
A metric space is plastic if all its non-expansive bijections are isometries. We prove three main results: (1) every countable dense subspace of a normed space is not plastic, (2)…
Expand-contract plasticity on the real line
Dirk Langemann, Olesia Zavarzina
The article deals with plastic and non-plastic sub-spaces of the real line with the usual Euclidean metric . It investigates non-expansive bijections, proves…
Plastic pairs of metric spaces
Vladimir Kadets, Olesia Zavarzina
We address pairs of metric spaces with the following property: for every mapping the existence of points with implies the…
On expand-contract plasticity in quasi-metric spaces
Olesia Zavarzina
It is known that if any function acting from precompact metric space to itself increases the distance between some pair of points then it must decrease distance between some other…
Linear Expand-Contract Plasticity of Ellipsoids Revisited
Iryna Karpenko, Olesia Zavarzina
This work is aimed to describe linear expand-contract plastic ellipsoids given via quadratic form of a bounded positively defined self-adjoint operator in terms of its spectrum.
Two new examples of Banach spaces with a plastic unit ball
Rainis Haller, Nikita Leo, Olesia Zavarzina
We prove that Banach spaces and , with strictly convex and , have plastic unit balls (we call a metric space plastic if every no…
Generalized-lush spaces revisited
Vladimir Kadets, Olesia Zavarzina
We study geometric properties of GL-spaces. We demonstrate that every finite-dimensional GL-space is polyhedral; that in dimension 2 there are only two, up to isometry, GL-spaces,…
Linear expand-contract plasticity of ellipsoids in separable Hilbert spaces
Olesia Zavarzina
The paper is aimed to establish the interdependence between linear expand-contract plasticity of an ellipsoid in a separable Hilbert spaces and properties of the set of its semi-ax…
Non-expansive bijections, uniformities and polyhedral faces
Carlos Angosto, Vladimir Kadets, Olesia Zavarzina
We extend the result of B. Cascales at al. about expand-contract plasticity of the unit ball of strictly convex Banach space to those spaces whose unit ball is the union of all its…
Non-expansive bijections to the unit ball of -sum of strictly convex Banach spaces
Vladimir Kadets, Olesia Zavarzina
Extending recent results by Cascales, Kadets, Orihuela and Wingler (2016), Kadets and Zavarzina (2017), and Zavarzina (2017) we demonstrate that for every Banach space and ever…
Non-expansive bijections between unit balls of Banach spaces (A technical version with some boring proofs included)
Olesia Zavarzina
It is known that if is a finite-dimensional Banach space, or a strictly convex space, or the space , then every non-expansive bijection is an isometry.…