Absolutely p-summing operators and Banach spaces containing all uniformly complemented
Absolutely P-Summing, P-Nuclear Operators and Their Conjugates.
Absolutely summing operators in -spaces and their applications
Abstract characterization of Orlicz-Kantorovich lattices associated with an -valued measure
An abstract characterization of Orlicz-Kantorovich lattices constructed by a measure with values in the ring of measurable functions is presented.
Abstract multiplication semigroups.
Acción dual de las copias, isométricas asintóticamente, de lp (1 ≤ p < ∞) y c0.
Acknowledgement of priority: Separable quotients of Banach spaces.
In previous papers, it is proved, among other things, that every infinite dimensional sigma-Dedekind complete Banach lattice has a separable quotient. It has come to my attention that L. Weis proved this result without assuming sigma-Dedekind completeness; the proof is based, however, on the deep theorem of J. Hagler and W.B. Johnson concerning the structure of dual balls of Banach spaces and therefore cannot be applied simply to the case of locally convex solid topologically complete Riesz spaces....
Acknowledgment of priority to the paper "On self-conjugate Banach spaces''
Addendum to: "Linear operations, tensor products, and contractive projections in function spaces" (Studia Math. 38 (1970), pp. 131-186)
Addendum to "Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces" (Colloq. Math. 127 (2012), 105-109)
It is well known that if φ(t) ≡ t, then the system is not a Schauder basis in L₂[0,1]. It is natural to ask whether there is a function φ for which the power system is a basis in some Lebesgue space . The aim of this short note is to show that the answer to this question is negative.
Addendum to the paper "On isomorphisms of anisotropic Sobolev spaces with "classical Banach spaces" and a Sobolev type embedding theorem"
Addendum to the paper The Projecitve Tenso Product II: The Radon-Nikodym Property.
Adequate Compacta which are Gul’ko or Talagrand
2000 Mathematics Subject Classification: 54H05, 03E15, 46B26We answer positively a question raised by S. Argyros: Given any coanalytic, nonalytic subset Σ′ of the irrationals, we construct, in Mercourakis space c1(Σ′), an adequate compact which is Gul’ko and not Talagrand. Further, given any Borel, non Fσ subset Σ′ of the irrationals, we construct, in c1(Σ′), an adequate compact which is Talagrand and not Eberlein.Supported by grants AV CR 101-90-03, and GA CR 201-01-1198
Affine bijections of C(X,I)
Let 𝒳 be a compact Hausdorff space which satisfies the first axiom of countability, I = [0,1] and 𝓒(𝒳,I) the set of all continuous functions from 𝒳 to I. If φ: 𝓒(𝒳,I) → 𝓒(𝒳,I) is a bijective affine map then there exists a homeomorphism μ: 𝒳 → 𝒳 such that for every component C in 𝒳 we have either φ(f)(x) = f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C, or φ(f)(x) = 1-f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C.
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...
Algebraic and topological properties of some sets in ℓ₁
For a sequence x ∈ ℓ₁∖c₀₀, one can consider the set E(x) of all subsums of the series . Guthrie and Nymann proved that E(x) is one of the following types of sets: () a finite union of closed intervals; () homeomorphic to the Cantor set; homeomorphic to the set T of subsums of where b(2n-1) = 3/4ⁿ and b(2n) = 2/4ⁿ. Denote by ℐ, and the sets of all sequences x ∈ ℓ₁∖c₀₀ such that E(x) has the property (ℐ), () and ( ), respectively. We show that ℐ and are strongly -algebrable and is -lineable. We...
Algebraic reflexivity of C(X,E) and Cambern's theorem
The algebraic and topological reflexivity of C(X) and C(X,E) are investigated by using representations for the into isometries due to Holsztyński and Cambern.
Algebres à bases bornées.
Algunos resultados sobre representabilidad finita de 1q (O < q ≤∞) en espacios p-Banach.
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.