Mazur spaces.
Metric convexity and normability of metric linear spaces
Metric criteria for Banach and Euclidean spaces
Metrically convex functions in normed spaces
Properties of metrically convex functions in normed spaces (of any dimension) are considered. The main result, Theorem 4.2, gives necessary and sufficient conditions for a function to be metrically convex, expressed in terms of the classical convexity theory.
Multi-normed spaces [Book]
Nature de l'image linéaire continue d'un espace de Banach dans un espace de Banach séparable
Necessary and sufficient condition for compactness of the embedding operator.
New concepts in nondifferentiable programming
Non-archimedean representations of compact groups
Nonexpansive retracts in Banach spaces
We study various aspects of nonexpansive retracts and retractions in certain Banach and metric spaces, with special emphasis on the compact nonexpansive envelope property.
Nonseparable "James tree" analogues of the continuous functions on the Cantor set
Normed spaces over valued fields.
Note on bi-Lipschitz embeddings into normed spaces
Let , be metric spaces and an injective mapping. We put , and (the distortion of the mapping ). We investigate the minimum dimension such that every -point metric space can be embedded into the space with a prescribed distortion . We obtain that this is possible for , where is a suitable absolute constant. This improves a result of Johnson, Lindenstrauss and Schechtman [JLS87] (with a simpler proof). Related results for embeddability into are obtained by a similar method.
Note on separation of convex sets
O některých Banachových problémech
On (a,b,c,d)-orthogonality in normed linear spaces
We first introduce a notion of (a,b,c,d)-orthogonality in a normed linear space, which is a natural generalization of the classical isosceles and Pythagorean orthogonalities, and well known α- and (α,β)-orthogonalities. Then we characterize inner product spaces in several ways, among others, in terms of one orthogonality implying another orthogonality.
On Banach spaces X for which
On Biorthogonal Systems and Total Sequences of Functionals. II.
On Carathéodory's and Krein-Milman's theorems in fully ordered groups
On coarse embeddability into -spaces and a conjecture of Dranishnikov
We show that the Hilbert space is coarsely embeddable into any for 1 ≤ p ≤ ∞. It follows that coarse embeddability into ℓ₂ and into are equivalent for 1 ≤ p < 2.