A reflexive Banach space which is not sufficiently Euclidean
A remark on functions continuous on all lines
We prove that each linearly continuous function on (i.e., each function continuous on all lines) belongs to the first Baire class, which answers a problem formulated by K. C. Ciesielski and D. Miller (2016). The same result holds also for on an arbitrary Banach space , if has moreover the Baire property. We also prove (extending a known finite-dimensional result) that such on a separable is continuous at all points outside a first category set which is also null in any usual sense.
A short proof of Dvoretzky's theorem
A short remark on Kolmogoroff normability theorem.
A Simple Proof of the Dauns-Hofmann Theorem.
A weakly pseudocompact subspace of Banach space is weakly compact
Absolutely P-Summing, P-Nuclear Operators and Their Conjugates.
Affine group acting on hyperspaces of compact convex subsets of ℝⁿ
For every n ≥ 2, let cc(ℝⁿ) denote the hyperspace of all nonempty compact convex subsets of the Euclidean space ℝⁿ endowed with the Hausdorff metric topology. Let cb(ℝⁿ) be the subset of cc(ℝⁿ) consisting of all compact convex bodies. In this paper we discover several fundamental properties of the natural action of the affine group Aff(n) on cb(ℝⁿ). We prove that the space E(n) of all n-dimensional ellipsoids is an Aff(n)-equivariant retract of cb(ℝⁿ). This is applied to show that cb(ℝⁿ) is homeomorphic...
Algunos resultados sobre sistemas de desigualdades lineales.
En este artículo aplicamos la condición de Mazur-Orlicz para extender a espacios normados algunos resultados de consistencia de desigualdades lineales (s.d.l.) en Rn. Asimismo, obtenemos condiciones para la consistencia de s.d.l. en un espacio localmente convexo, cuando las soluciones pertenecen a ciertos subconjuntos del dual topológico.
An approach to generalizing Banach spaces: normed almost linear spaces
An Elementary Characterization of Absolutely Summing Operators.
An extension of Lorentz's almost convergence and applications in Banach spaces
2000 Mathematics Subject Classification: Primary 40C99, 46B99.We investigate an extension of the almost convergence of G. G. Lorentz requiring that the means of a bounded sequence converge uniformly on a subset M of N. We also present examples of sequences α∈ l∞(N) whose sequences of translates (Tn α)n≥ 0 (where T is the left-shift operator on l∞(N)) satisfy: (a) Tn α, n ≥ 0 generates a subspace E(α) of l∞(N) that is isomorphically embedded into c0 while α is not almost convergent. (b) Tn...
An isomorphic characterization of the Schmidt class
Analytic sheaves in Banach spaces
Angles in metric and normed linear spaces
Antiproximinal sets in the Banach space
If is a Banach space then the Banach space of all -valued convergent sequences contains a nonvoid bounded closed convex body such that no point in has a nearest point in .
Application des ultraproduits à l'étude des espaces et des algèbres de Banach
Applications des ultraproduits à la théorie des plongements des espaces de Banach
Approximation des bornés d'un espace de Banach par des compacts et applications
Approximation des optima de Pareto