Mikhail I. Ostrovskii

Learn More
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(B X , B Y) between the respective closed unit balls over all isometric linear embeddings of X and Y into a common Banach space Z. This is compared with the(More)
For a Banach space X we shall denote the set of all closed subspaces of X by G(X). In some kinds of problems it turned out to be useful to endow G(X) with a topology. The main purpose of the present paper is to survey results on two the most common topologies on G(X). The organization of this paper is as follows. In section 2 we introduce some definitions(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. A metric space (M, d(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 main purpose of the present paper is(More)