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Extremal properties of the set of vector-valued Banach limits

Francisco Javier García-Pacheco (2015)

Open Mathematics

In this manuscript we find another class of real Banach spaces which admit vector-valued Banach limits different from the classes found in [6, 7]. We also characterize the separating subsets of ℓ∞(X). For this we first need to study when the space of almost convergent sequences is closed in the space of bounded sequences, which turns out to happen only when the underlying space is complete. Finally, a study on the extremal structure of the set of vector-valued Banach limits is conducted when the...

Extremal sections of complex l p -balls, 0 < p ≤ 2

Alexander Koldobsky, Marisa Zymonopoulou (2003)

Studia Mathematica

We study the extremal volume of central hyperplane sections of complex n-dimensional l p -balls with 0 < p ≤ 2. We show that the minimum corresponds to hyperplanes orthogonal to vectors ξ = (ξ¹,...,ξⁿ) ∈ ℂⁿ with |ξ¹| = ... = |ξⁿ|, and the maximum corresponds to hyperplanes orthogonal to vectors with only one non-zero coordinate.

Extremal solutions of a general marginal problem

Petra Linhartová (1991)

Commentationes Mathematicae Universitatis Carolinae

The characterization of extremal points of the set of probability measures with given marginals is given in the general context of a marginal system. The sets of marginal uniqueness are studied and an example is added to illustrate the theory.

Extreme and exposed representing measures of the disk algebra

Alex Heinis, Jan Wiegerinck (2000)

Annales Polonici Mathematici

We study the extreme and exposed points of the convex set consisting of representing measures of the disk algebra, supported in the closed unit disk. A boundary point of this set is shown to be extreme (and even exposed) if its support inside the open unit disk consists of two points that do not lie on the same radius of the disk. If its support inside the unit disk consists of 3 or more points, it is very seldom an extreme point. We also give a necessary condition for extreme points to be exposed...

Extreme cases of weak type interpolation.

Evgeniy Pustylnik (2005)

Revista Matemática Iberoamericana

We consider quasilinear operators T of joint weak type (a, b; p, q) (in the sense of [2]) and study their properties on spaces Lφ,E with the norm||φ(t) f*(t)||Ê, where Ê is arbitrary rearrangement-invariant space with respect to the measure dt/t. A space Lφ,E is said to be "close" to one of the endpoints of interpolation if the corresponding Boyd index of this space is equal to 1/a or to 1/p. For all possible kinds of such "closeness", we give sharp estimates for the function ψ(t) so as to obtain...

Extreme compact operators from Orlicz spaces to C ( Ω )

Shutao Chen, Marek Wisła (1993)

Commentationes Mathematicae Universitatis Carolinae

Let E ϕ ( μ ) be the subspace of finite elements of an Orlicz space endowed with the Luxemburg norm. The main theorem says that a compact linear operator T : E ϕ ( μ ) → C ( Ω ) is extreme if and only if T * ω ∈ Ext B ( ( E ϕ ( μ ) ) * ) on a dense subset of Ω , where Ω is a compact Hausdorff topological space and 〈 T * ω , x 〉 = ( T x ) ( ω ) . This is done via the description of the extreme points of the space of continuous functions C ( Ω , L ϕ ( μ ) ) , L ϕ ( μ ) being an Orlicz space equipped with the Orlicz norm (conjugate to the Luxemburg one). There is also given a theorem on closedness of the set of extreme...

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