Displaying similar documents to “On a problem of Banach”

Distances between Hilbertian operator spaces

Seán Dineen, Cristina Radu (2014)

Studia Mathematica

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We compute the completely bounded Banach-Mazur distance between different finite-dimensional homogeneous Hilbertian operator spaces.

Homogenous Banach spaces on the unit circle.

Thomas Vils Pedersen (2000)

Publicacions Matemàtiques

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We prove that a homogeneous Banach space B on the unit circle T can be embedded as a closed subspace of a dual space Ξ*B contained in the space of bounded Borel measures on T in such a way that the map B → Ξ*B defines a bijective correspondence between the class of homogeneous Banach spaces on T and the class of prehomogeneous Banach spaces on T. We apply our results to show that the algebra of all continuous functions on T is the only...

Metric spaces with the small ball property

Ehrhard Behrends, Vladimir M. Kadets (2001)

Studia Mathematica

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A metric space (M,d) is said to have the small ball property (sbp) if for every ε₀ > 0 it is possible to write M as the union of a sequence (B(xₙ,rₙ)) of closed balls such that the rₙ are smaller than ε₀ and lim rₙ = 0. We study permanence properties and examples of sbp. The main results of this paper are the following: 1. Bounded convex closed sets in Banach spaces have sbp only if they are compact. 2. Precisely the finite-dimensional Banach spaces have sbp. (More generally: a complete...

Linearly rigid metric spaces and the embedding problem

J. Melleray, F. V. Petrov, A. M. Vershik (2008)

Fundamenta Mathematicae

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We consider the problem of isometric embedding of metric spaces into Banach spaces, and introduce and study the remarkable class of so-called linearly rigid metric spaces: these are the spaces that admit a unique, up to isometry, linearly dense isometric embedding into a Banach space. The first nontrivial example of such a space was given by R. Holmes; he proved that the universal Urysohn space has this property. We give a criterion of linear rigidity of a metric space, which allows...