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.
Reflexivity of the isometry group of some classical spaces.
We investigate the reflexivity of the isometry group and the automorphism group of some important metric linear spaces and a1gebras. The paper consists of the following sections: 1. Preliminaries. 2. Sequence spaces. 3. Spaces of measurable functions. Hardy spaces. 5. Banach algebras of holomorphic functions. 6. Fréchet algebras of holomorphic functions. 7. Spaces of continuous functions.
Regards sur le problème des rotations de Mazur.
Regular hexagons in normed spaces and a theorem of Walter Benz.
Réitération de modèles étalés
Relation between fixed point and asymptotical center of nonexpansive maps.
Relative rotundity in Lp(X).
Remarks and examples concerning distance ellipsoids
We provide for every 2 ≤ k ≤ n an n-dimensional Banach space E with a unique distance ellipsoid such that there are precisely k linearly independent contact points between and . The corresponding result holds for spaces with non-unique distance ellipsoids as well. We construct n-dimensional Banach spaces E such that one distance ellipsoid has precisely k linearly independent contact points and all other distance ellipsoids have less than k-1 such points.
Remarks on asymptotic centers and fixed points.
Remarks on embeddable semigroups in groups and a generalization of some Cuthbert's results.
Remarks on orthogonality preserving mappings in normed spaces and some stability problems.
Remarks on remotal sets in vector valued function spaces.
Remarks on rich subspaces of Banach spaces
We investigate rich subspaces of L₁ and deduce an interpolation property of Sidon sets. We also present examples of rich separable subspaces of nonseparable Banach spaces and we study the Daugavet property of tensor products.
Remarks on some properties in the geometric theory of Banach spaces
The aim of this paper is to derive some relationships between the concepts of the property of strong introduced recently by Hong-Kun Xu and the so-called characteristic of near convexity defined by Goebel and Sȩkowski. Particularly we provide very simple proof of a result obtained by Hong-Kun Xu.
Remarks on the complementability of spaces of Bochner integrable functions in spaces of vector measures
In the paper [5] L. Drewnowski and the author proved that if is a Banach space containing a copy of then is not complemented in and conjectured that the same result is true if is any Banach space without the Radon-Nikodym property. Recently, F. Freniche and L. Rodriguez-Piazza ([7]) disproved this conjecture, by showing that if is a finite measure and is a Banach lattice not containing copies of , then is complemented in . Here, we show that the complementability of in together...
Remarks on the Istratescu measure of noncompactness.
In this paper we give estimations of Istratescu measure of noncompactness I(X) of a set X C lp(E1,...,En) in terms of measures I(Xj) (j=1,...,n) of projections Xj of X on Ej. Also a converse problem of finding a set X for which the measure I(X) satisfies the estimations under consideration is considered.
Remarques sur un résultat non publié de B. Maurey
Renorming Banach spaces with many projections and smoothness properties.
Renorming Concerning Mazur's Intersection Property of Balls for Weakly Compact Convex Sets.
Report on twisted sums of Banach spaces.
This note is to report some of the advances obtained as a follow-up of the book [2] on the topic of twisted sums of Banach spaces. Since this announcement is no longer enough to contain the theory being developed, we submit the interested reader to [2] and to [1], where full details and proofs shall appear.