Unique reducibility of subsets of commutative topological groups and semigroups.
Uniquely Generated Grothendieck Space Ideals.
Uniqueness condition for the Pick problem.
Uniqueness of Cartesian Products of Compact Convex Sets
Let , i∈ I, and , j∈ J, be compact convex sets whose sets of extreme points are affinely independent and let φ be an affine homeomorphism of onto . We show that there exists a bijection b: I → J such that φ is the product of affine homeomorphisms of onto , i∈ I.
Uniqueness of Hahn-Banach extensions and liftings of linear dependences.
Uniqueness of Hahn-Banach Extensions from Certain Spaces of Analytic Functions.
Uniqueness of invariant Hahn-Banach extensions.
Uniqueness of Representation Spaces.
Uniqueness of unconditional bases of , 0 < p < 1
We prove that if 0 < p < 1 then a normalized unconditional basis of a complemented subspace of must be equivalent to a permutation of a subset of the canonical unit vector basis of . In particular, has unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss, and Tzafriri have previously proved the same result for .
Uniqueness of unconditional basis of and , 0 < p < 1
We prove that the quasi-Banach spaces and (0 < p < 1) have a unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss and Tzafriri have previously proved that the same is true for the respective Banach envelopes and ℓ₁(ℓ₂). They used duality techniques which are not available in the non-locally convex case.
Unital Embedding and Complexification of F-Algebras.
Unitary sequences and classes of barrelledness.
It is well known that some dense subspaces of a barrelled space could be not barrelled. Here we prove that dense subspaces of l∞ (Ω, X) are barrelled (unordered Baire-like or p?barrelled) spaces if they have ?enough? subspaces with the considered barrelledness property and if the normed space X has this barrelledness property.These dense subspaces are used in measure theory and its barrelledness is related with some sequences of unitary vectors.
Universal spaces and universal bases in metric spaces
Universal stability of Banach spaces for ε -isometries
Let X, Y be real Banach spaces and ε > 0. A standard ε-isometry f: X → Y is said to be (α,γ)-stable (with respect to for some α,γ > 0) if T is a linear operator with ||T|| ≤ α such that Tf- Id is uniformly bounded by γε on X. The pair (X,Y) is said to be stable if every standard ε-isometry f: X → Y is (α,γ)-stable for some α,γ > 0. The space X[Y] is said to be universally left [right]-stable if (X,Y) is always stable for every Y[X]. In this paper, we show that universally right-stable...
Unordered Baire-like spaces without local convexity.
The aim of the present paper is to study the class of tvs which we define by ommiting the word increasing in the definition of *-suprabarrelled spaces. We prove that the product of Baire tvs is *-UBL and hence the class of *-UBL spaces is stricty larger than the class of Baire spaces.
Unordered Baire-like vector-valued function spaces.
Upper Semi-Continuity of Convex Functions and Openness of Affine Maps.
Utilisation de limites inductives généralisées d'espaces localement convexes