Bilipschitz mappings and strong weights.
Binormality of Banach spaces
We study binormality, a separation property of spaces endowed with two topologies known in the real analysis as the Luzin-Menchoff property. The main object of our interest are Banach spaces with their norm and weak topologies. We show that every separable Banach space is binormal and the space is not binormal.
Bisectors in Minkowski 3-space.
Bochner property in Banach spaces
Boundary of polyhedral spaces: an alternative proof.
A Banach space X is called polyhedral if the unit ball of each one of its finite-dimensional (equivalently: two-dimensional [6]) subspaces is a polytope. Polyhedral spaces were studied by various authors; most of the structural results are due to V. Fonf. We refer the reader to the surveys [1], [2] for other definitions of polyhedrality, main properties and bibliography. In this paper we present a short alternative proof of the basic result on the structure of the unit ball of the polyhedral space...
Bounded analytic sets in Banach spaces
Conditions are given which enable or disable a complex space to be mapped biholomorphically onto a bounded closed analytic subset of a Banach space. They involve on the one hand the Radon-Nikodym property and on the other hand the completeness of the Caratheodory metric of .
Bounded Holomorphic Embeddings of the Unit Disk into Banach Spaces.
Boundedness and surjectivity in normed spaces.
Boundedness of linear maps
In this short note we consider necessary and sufficient conditions on normed linear spaces, that ensure the boundedness of any linear map whose adjoint maps extreme points of the unit ball of the domain space to continuous linear functionals.
Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces.
B-выпуклость и неустойчивость неполноты.
c0, l1 and l∞ in function spaces.
Calkin algebras for Banach spaces with finitely decomposable quotients
For a Banach space X such that all quotients only admit direct decompositions with a number of summands smaller than or equal to n, we show that every operator T on X can be identified with an n × n scalar matrix modulo the strictly cosingular operators SC(X). More precisely, we obtain an algebra isomorphism from the Calkin algebra L(X)/SC(X) onto a subalgebra of the algebra of n × n scalar matrices which is triangularizable when X is indecomposable. From this fact we get some information on the...
Caractérisations de sous-espaces normés de de dimension finie
Characteristic of convexity of Köthe function spaces.
Characteristic of convexity of Musielak-Orlicz function spaces equipped with the Luxemburg norm
In this paper we extend the result of [6] on the characteristic of convexity of Orlicz spaces to the more general case of Musielak-Orlicz spaces over a non-atomic measure space. Namely, the characteristic of convexity of these spaces is computed whenever the Musielak-Orlicz functions are strictly convex.
Characterization of intermediate values of the triangle inequality II
In [Mineno K., Nakamura Y., Ohwada T., Characterization of the intermediate values of the triangle inequality, Math. Inequal. Appl., 2012, 15(4), 1019–1035] there was established a norm inequality which characterizes all intermediate values of the triangle inequality, i.e. C n that satisfy 0 ≤ C n ≤ Σj=1n ‖x j‖ − ‖Σj=1n x j‖, x 1,...,x n ∈ X. Here we study when this norm inequality attains equality in strictly convex Banach spaces.
Characterization of normed linear spaces with generalized Mazur intersection property
Let 𝓐 be a compatible collection of bounded subsets in a normed linear space. We give a characterization of the following generalized Mazur intersection property: every closed convex set A ∈ 𝓐 is an intersection of balls.
Characterization of Strongly Exposed Points in General Köthe-Bochner Banach Spaces
We study strongly exposed points in general Köthe-Bochner Banach spaces X(E). We first give a characterization of strongly exposed points of the set of X-selections of a measurable multifunction Γ. We then apply this result to the study of strongly exposed points of the closed unit ball of X(E). Precisely we show that if an element f is a strongly exposed point of , then |f| is a strongly exposed point of and f(ω)/∥ f(ω)∥ is a strongly exposed point of for μ-almost all ω ∈ S(f).
Characterization of the strict convexity of the Besicovitch-Musielak-Orlicz space of almost periodic functions
We introduce the new class of Besicovitch-Musielak-Orlicz almost periodic functions and consider its strict convexity with respect to the Luxemburg norm.