1,720,959 research outputs found
Isometric Structure of Transportation Cost Spaces on Finite Metric Spaces
No full textOstrovskii, Mikhail/0000-0002-7164-196XThe paper is devoted to isometric Banach-space- theoretical structure of transportation cost (TC) spaces on finite metric spaces. The TC spaces arc also known as Arens-Eells, Lipschitzfree, or Wasserstein spaces. A new notion of a roadmap pertinent to a transportation problem on a finite metric space has been introduced and used to simplify proofs for the results on representation of TC spaces as quotients of l(1) spaces on the edge set over the cycle space. A Tolstoi-type theorem for roadmaps is proved, and directed subgraphs of the canonical graphs, which are supports of maximal optimal roadmaps, are characterized. Possible obstacles for a TC space on a finite metric space X preventing them from containing subspaces isometric to l(infinity)(n) have been found in terms of the canonical graph of X. The fact that TC spaces on diamond graphs do not contain l(infinity)(4) isometrically has been derived. In addition, a short overview of known results on the isometric structure of TC spaces on finite metric spaces is presented.Atilim University; National Science Foundation [NSF DMS-1953773]The first-named author gratefully acknowledges the support by Atilim University. This paper was written while the first-named author was on research leave supported by Atilim University. The second-named author gratefully acknowledges the support by the National Science Foundation grant NSF DMS-1953773. The authors express their sincere gratitude to the anonymous referee for the useful suggestions and important pointers to the literature
Universality and Non-Embeddability Into Banach Spaces of Subspaces of the Real Line With the Gromov-Hausdorff Distance
No full textThe 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.National Science Foundation [NSF DMS-1953773]; National Science FoundationThe second-named author gratefully acknowledges the support by the National Science Foundation grant NSF DMS-1953773. The authors express their sincere gratitude to the anonymous referees for their valuable comments and suggestions, all of which helped us to improve the paper.Science Citation Index Expande
On Embeddings of Locally Finite Metric Spaces Into <i>l<sub>p</Sub><
No full textIt is known that if finite subsets of a locally finite metric space M admit C-bilipschitz embeddings into l(p) (1 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.National Science Foundation [NSF DMS-1700176]The second-named author gratefully acknowledges the support by National Science Foundation grant NSF DMS-1700176
Complementability of Isometric Copies of L1 in Transportation Cost Spaces
Full text linkThis 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.National Science Foundation [NSF DMS-1953773]The second-named author gratefully acknowledges the support by the National Science Foundation grant NSF DMS-1953773. The authors express their sincere gratitude to the referee for constructive criticism and many helpful comments
Nonexistence of Embeddings With Uniformly Bounded Distortions of Laakso Graphs Into Diamond Graphs
No full textDiamond 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.National Science Foundation [DMS-1201269]; St. John's UniversityThe second-named author gratefully acknowledges the support by National Science Foundation DMS-1201269 and by Summer Support of Research program of St. John's University during different stages of work on this paper. The authors thank Siu Lam Leung for his valuable comments and the reviewer for many valuable suggestions and critical comments
On Relations Between Transportation Cost Spaces and <i>l</I><sub>1<
Full text linkThe 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.National Science Foundation [NSF DMS-1700176]; St. John's UniversityThe second author gratefully acknowledges the support by the National Science Foundation grant NSF DMS-1700176 and by St. John's University. We would like to thank the referee for the careful reading of the paper and numerous corrections
Dvoretzky-Type Theorem for Locally Finite Subsets of a Hilbert Space
No full textThe 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.Atilim University; National Science Foundation [NSF DMS-1953773]The second-named author gratefully acknowledges the support of Atilim University as this work was mostly conducted while she was on research leave supported by Atilim University. Also, she expresses her sincere gratitude to professor G. M. Feldman (B.Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine) for his invitation to the Department of Function Theory for this research leave and his help during her stay at the Department. The third-named author gratefully acknowledges the support by the National Science Foundation grant NSF DMS-1953773
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Weak closures and derived sets in dual Banach spaces
Full text linkThe main results of the paper: \textbf{(1)} The dual Banach space contains a linear subspace such that the set of all limits of weak convergent bounded nets in is a proper norm-dense subset of if and only if is a non-quasi-reflexive Banach space containing an infinite-dimensional subspace with separable dual. \textbf{(2)} Let be a non-reflexive Banach space. Then there exists a convex subset such that (the latter denotes the weak closure of ). \textbf{(3)} Let be a quasi-reflexive Banach space and be an absolutely convex subset. Then
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