M. I. Ostrovskii

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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)
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)
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)
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)
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)
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)