Quantitative unconditionality of Banach spaces E for which K(E) is an M-ideal in ℒ(E)
Quasi-Banach Spaces which are Unique Predual.
Quasi-reflexive Banach spaces
Quelques propriétés des espaces de Banach stables
Quelques remarques sur la propriété (C) des espaces de Banach
Quelques résultats concernant l'inconditionnalité
Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces
On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if and only if each everywhere defined quotient of two continuous convex functions is a d.c. function. Our construction also gives a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals.
Reflexive Banach space and fixed point theorems.
Reflexive Banach spaces without equivalent norms which are uniformly convex or uniformly differentiable in every direction
Reflexive invariant subspaces of L... (G) are finite dimensional.
Reflexive Orlicz spaces have uniformly normal structure
We prove that an Orlicz space equipped with the Luxemburg norm has uniformly normal structure if and only if it is reflexive.
Reflexive spaces and numerical radius attaining operators.
In this note we deal with a version of James' Theorem for numerical radius, which was already considered in [4]. First of all, let us recall that this well known classical result states that a Banach space satisfying that all the (bounded and linear) functionals attain the norm, has to be reflexive [16].
Reflexive subspaces of some Orlicz spaces
We show that when the conjugate of an Orlicz function ϕ satisfies the growth condition Δ⁰, then the reflexive subspaces of are closed in the L¹-norm. For that purpose, we use (and give a new proof of) a result of J. Alexopoulos saying that weakly compact subsets of such have equi-absolutely continuous norm.
Reflexivität und Schauder Basen vom Typ P und P in lokalkonvexen Räumen.
Reflexivity and approximate fixed points
A Banach space X is reflexive if and only if every bounded sequence xₙ in X contains a norm attaining subsequence. This means that it contains a subsequence for which is attained at some f in the dual unit sphere . A Banach space X is not reflexive if and only if it contains a normalized sequence xₙ with the property that for every , there exists such that . Combining this with a result of Shafrir, we conclude that every infinite-dimensional Banach space contains an unbounded closed convex...
Regular maximal monotone operators and the sum theorem.
Remarks on Strict Monotonicity and Surjectivity Properties of Duality Mappings Definied on Real Normed Linear Spaces.
Renorming Concerning Mazur's Intersection Property of Balls for Weakly Compact Convex Sets.
Rotundity and smoothness of convex bodies in reflexive and nonreflexive spaces
For combining two convex bodies C and D to produce a third body, two of the most important ways are the operation ∓ of forming the closure of the vector sum C+D and the operation γ̅ of forming the closure of the convex hull of C ⋃ D. When the containing normed linear space X is reflexive, it follows from weak compactness that the vector sum and the convex hull are already closed, and from this it follows that the class of all rotund bodies in X is stable with respect to the operation ∓ and the class...
Schauder bases and reflexivity