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- M. I. Ostrovskii
- Discrete Mathematics
- 2004

Let G be a graph and let T be a tree with the same vertex set. Let e be an edge of T and Ae and Be be the vertex sets of the components of T obtained after removal of e. Let EG(Ae, Be) be the set of edges of G with one endvertex in Ae and one endvertex in Be. Let ec(G : T ) := max e |EG(Ae, Be)|. The paper is devoted to minimization of ec(G : T ) • Over all… (More)

- N J Kalton, M I Ostrovskii
- 1997

Abstract. The main object of the paper is to study the distance between Banach spaces introduced by Kadets. For Banach spaces X and Y , the Kadets distance is defined to be the infimum of the Hausdorff distance d(BX , BY ) between the respective closed unit balls over all isometric linear embeddings of X and Y into a common Banach space Z. This is compared… (More)

- M I Ostrovskii
- 1993

It is proved that there exist complemented subspaces of countable topological products (locally convex direct sums) of Banach spaces which cannot be represented as topological products (locally convex direct sums) of Banach spaces The problem of description of complemented subspaces of a given locally convex space is one of the general problems of structure… (More)

- M. I. Ostrovskii
- 2004

max(u,v)∈E |f(u)− f(v)| if p =∞. If G is connected, then the only functions f satisfying ||f ||E,p = 0 are constant functions, so || · ||E,p is a norm on each linear space of functions on VG which does not contain constants. Usually we shall consider the subspace in the space of all functions on VG given by ∑ v∈V f(v)dv = 0. The obtained normed space will… (More)

- M. I. Ostrovskii
- 2007

The first problem considered in this paper: is it possible to find upper estimates for the spanning tree congestion for bipartite graphs which are better than for general graphs? It is proved that there exists a bipartite version of the known graph with spanning tree congestion of order n 3 2 , where n is the number of vertices. The second problem is to… (More)

- M. I. Ostrovskii
- 2009

The main purpose of the paper is to find some expansion properties of locally finite metric spaces which do not embed coarsely into a Hilbert space. The obtained result is used to show that infinite locally finite graphs excluding a minor embed coarsely into a Hilbert space. In an appendix a direct proof of the latter result is given. 2000 Mathematics… (More)

- M I Ostrovskii
- 1994

X iv :m at h/ 93 03 20 2v 1 [ m at h. FA ] 2 9 M ar 1 99 3 TOPOLOGIES ON THE SET OF ALL SUBSPACES OF A BANACH SPACE AND RELATED QUESTIONS OF BANACH SPACE GEOMETRY M.I.OSTROVSKII

- M I Ostrovskii
- 2002

Definition. A symmetric with respect to 0 bounded closed convex set A in a finite dimensional normed space X is called a sufficient enlargement for X (or of B(X)) if for arbitrary isometric embedding of X into a Banach space Y there exists a projection P : Y → X such that P (B(Y )) ⊂ A (by B we denote the unit ball). The notion of sufficient enlargement is… (More)

- M. I. Ostrovskii
- 2011

The main purpose of the paper is to prove the following results: • Let A be a locally finite metric space whose finite subsets admit uniformly bilipschitz embeddings into a Banach space X. Then A admits a bilipschitz embedding into X. • Let A be a locally finite metric space whose finite subsets admit uniformly coarse embeddings into a Banach space X. Then… (More)

- M. I. Ostrovskii
- 2011

Let P be a class of Banach spaces and let T = {Tα}α∈A be a set of metric spaces. We say that T is a set of test-spaces for P if the following two conditions are equivalent: (1) X / ∈ P; (2) The spaces {Tα}α∈A admit uniformly bilipschitz embeddings into X. The first part of the paper is devoted to a simplification of the proof of the following test-space… (More)