Browsing by Author "Ostrovskii, Mikhail I."

Now showing 1 - 7 of 7

Citation - WoS: 3
Citation - Scopus: 3
Complementability of Isometric Copies of L1 in Transportation Cost Spaces
(Academic Press inc Elsevier Science, 2024) Ostrovska, Sofiya; Ostrovskii, Mikhail I.
This work aims to establish new results pertaining to the structure of transportation cost spaces. Due to the fact that those spaces were studied and applied in various contexts, they have also become known under different names such as Arens-Eells spaces, Lipschitz-free spaces, and Wasserstein spaces. The main outcome of this paper states that if a metric space X is such that the transportation cost space on X contains an isometric copy of L1, then it contains a 1-complemented isometric copy of $1. (c) 2023 Elsevier Inc. All rights reserved.
Dvoretzky-Type Theorem for Locally Finite Subsets of a Hilbert Space
(Annales Inst Fourier, 2025) Catrina, Florin; Ostrovska, Sofiya; Ostrovskii, Mikhail I.
The main result of the paper: Given any epsilon > 0, every locally finite subset of l(2) admits a (1 + epsilon)-bilipschitz embedding into an arbitrary infinite-dimensional Banach space. The result is based on two results which are of independent interest: (1) A direct sum of two finite-dimensional Euclidean spaces contains a sub-sum of a controlled dimension which is epsilon-close to a direct sum with respect to a 1-unconditional basis in a two-dimensional space. (2) For any finite-dimensional Banach space Y and its direct sum X with itself with respect to a 1-unconditional basis in a two-dimensional space, there exists a (1 + epsilon)-bilipschitz embedding of Y into X which on a small ball coincides with the identity map onto the first summand and on the complement of a large ball coincides with the identity map onto the second summand.
Citation - WoS: 15
Citation - Scopus: 14
Generalized Transportation Cost Spaces
(Springer Basel Ag, 2019) Ostrovska, Sofiya; Ostrovskii, Mikhail I.
The paper is devoted to the geometry of transportation cost spaces and their generalizations introduced by Melleray et al. (Fundam Math 199(2):177-194, 2008). Transportation cost spaces are also known as Arens-Eells, Lipschitz-free, or Wasserstein 1 spaces. In this work, the existence of metric spaces with the following properties is proved: (1) uniformly discrete metric spaces such that transportation cost spaces on them do not contain isometric copies of l(1), this result answers a question raised by Cuth and Johanis (Proc Am Math Soc 145(8):3409-3421, 2017); (2) locally finite metric spaces which admit isometric embeddings only into Banach spaces containing isometric copies of l(1); (3) metric spaces for which the double-point norm is not a norm. In addition, it is proved that the double-point norm spaces corresponding to trees are close to l(infinity)(d) of the corresponding dimension, and that for all finite metric spaces M, except a very special class, the infimum of all seminorms for which the embedding of M into the corresponding seminormed space is isometric, is not a seminorm.
Citation - WoS: 4
Citation - Scopus: 4
Nonexistence of Embeddings With Uniformly Bounded Distortions of Laakso Graphs Into Diamond Graphs
(Elsevier Science Bv, 2017) Ostrovska, Sofiya; Ostrovskii, Mikhail I.
Diamond graphs and Laakso graphs are important examples in the theory of metric embeddings. Many results for these families of graphs are similar to each other. In this connection, it is natural to ask whether one of these families admits uniformly bilipschitz embeddings into the other. The well-known fact that Laakso graphs are uniformly doubling but diamond graphs are not, immediately implies that diamond graphs do not admit uniformly bilipschitz embeddings into Laakso graphs. The main goal of this paper is to prove that Laakso graphs do not admit uniformly bilipschitz embeddings into diamond graphs. (C) 2016 Elsevier B.V. All rights reserved.
Citation - WoS: 4
Citation - Scopus: 5
On Embeddings of Locally Finite Metric Spaces Into l_p<
(Academic Press inc Elsevier Science, 2019) Ostrovska, Sofiya; Ostrovskii, Mikhail I.
It is known that if finite subsets of a locally finite metric space M admit C-bilipschitz embeddings into l(p) (1 <= p <= infinity), then for every epsilon > 0, the space M admits a (C + epsilon)-bilipschitz embedding into l(p). The goal of this paper is to show that for p not equal 2, infinity this result is sharp in the sense that e cannot be dropped out of its statement. (C) 2019 Elsevier Inc. All rights reserved.
Citation - WoS: 14
Citation - Scopus: 14
On Relations Between Transportation Cost Spaces and l_1<
(Academic Press inc Elsevier Science, 2020) Ostrovska, Sofiya; Ostrovskii, Mikhail I.
The present paper deals with some structural properties of transportation cost spaces, also known as Arens-Eells spaces, Lipschitz-free spaces and Wasserstein spaces. The main results of this work are: (1) A necessary and sufficient condition on an infinite metric space M, under which the transportation cost space on M contains an isometric copy of l(1). The obtained condition is applied to answer the open questions asked by Cuth and Johanis (2017) concerning several specific metric spaces. (2) The description of the transportation cost space of a weighted finite graph G as the quotient l(1) (E(G))/Z(G), where E(G) is the edge set and Z(G) is the cycle space of G. (C) 2020 Elsevier Inc. All rights reserved.
Universality and Non-Embeddability Into Banach Spaces of Subspaces of the Real Line With the Gromov-Hausdorff Distance
(Springer-Verlag Italia Srl, 2025) Ostrovska, Sofiya; Ostrovskii, Mikhail I.
The paper aims to prove two universality results which can be used to simplify some of the available proofs of non-embeddability results for the Gromov-Hausdorff metrics.