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On the Banach–Mazur Distance in Small Dimensions
We establish some results on the Banach–Mazur distance in small dimensions. Specifically, we determine the Banach–Mazur distance between the cube and...
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On the Banach-Mazur distance between continuous function spaces with scattered boundaries
We study the dependence of the Banach-Mazur distance between two subspaces of vector-valued continuous functions on the scattered structure of their...
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Relative growth rate and contact Banach–Mazur distance
In this paper, we define non-linear versions of Banach–Mazur distance in the contact geometry set-up, called contact Banach–Mazur distances and...
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Tingley’s problem for complex Banach spaces which do not satisfy the Hausdorff distance condition
In 2022, Hatori gave a sufficient condition for complex Banach spaces to have the complex Mazur–Ulam property. In this paper, we introduce a class of...
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Kottman-type results on separated sets
The following definition was introduced by R. Whitley in [Whi68] in order to deal with Banach’s problem asking whether two linearly isomorphic Banach...
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Complexity of distances: Reductions of distances between metric and Banach spaces
We show that all the standard distances from metric geometry and functional analysis, such as Gromov—Hausdorff distance, Banach—Mazur distance,...
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On Mazur rotations problem and its multidimensional versions
The article is a survey related to a classical unsolved problem in Banach space theory, appearing in Banach’s famous book in 1932, and known as the...
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Approximation Schemes for McKean–Vlasov and Boltzmann-Type Equations (Error Analysis in Total Variation Distance)
We deal with McKean–Vlasov and Boltzmann-type jump equations. This means that the coefficients of the stochastic equation depend on the law of the...
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On Banach–Mazur distance between planar convex bodies
Upper estimates of the diameter and the radius of the family of planar convex bodies with respect to the Banach–Mazur distance are obtained. Namely,...
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Constructions of Urysohn Universal Ultrametric Spaces
AbstractIn this paper, we give new constructions of Urysohn universal ultrametric spaces. We first characterize a Urysohn universal ultrametric...
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Extension of isometries from the unit sphere of a rank-2 Cartan factor
We prove that every surjective isometry from the unit sphere of a rank-2 Cartan factor C onto the unit sphere of a real Banach space Y , admits an...
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Variational Principles for Maximization Problems with Lower-semicontinuous Goal Functions
Let X be a completely regular topological space and f a real-valued bounded from above lower semicontinuous function in it. Let C ( X ) be the space of...
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On Wolfgang Lusky’s paper “The Gurarij spaces are unique”
This note surveys Wolfgang Lusky’s proof of uniqueness of the Gurariy spaces and mentions further developments.