Une remarque sur les espaces de Banach réticulés
Une structure uniforme faible remarquable, sur les cones faiblement complets.
Une topologie mixte sur l’espace
Uniform approximation of continuous functions and -functions in nuclear spaces by entire functions
Uniform bases in locally convex spaces.
Uniform boundedness principles for ordered topological vector spaces.
Uniform convexity and associate spaces
We prove that the associate space of a generalized Orlicz space is given by the conjugate modular even without the assumption that simple functions belong to the space. Second, we show that every weakly doubling -function is equivalent to a doubling -function. As a consequence, we conclude that is uniformly convex if and are weakly doubling.
Uniform homeomorphisms between Banach spaces
Uniform Kadec-Klee property and nearly uniform convexity in Köthe-Bochner sequence spaces
The uniformly Kadec-Klee property in Köthe-Bochner sequence spaces , where is a Köthe sequence space and is an arbitrary separable Banach space, is studied. Namely, the question of whether or not this geometric property lifts from and to is examined. It is settled affirmatively in contrast to the case when is a Köthe function space. As a corollary we get criteria for to be nearly uniformly convex.
Uniformity in weak convergence with respect to balls in Banach spaces.
Uniformly -continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces
Some class of locally solid topologies (called uniformly -continuous) on Köthe-Bochner spaces that are continuous with respect to some natural two-norm convergence are introduced and studied. A characterization of uniformly -continuous topologies in terms of some family of pseudonorms is given. The finest uniformly -continuous topology on the Orlicz-Bochner space is a generalized mixed topology in the sense of P. Turpin (see [11, Chapter I]).
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 .