Formes sous-linéaires minimales
Fortsetzungen von C...-Funktionen, welche auf einer abgeschlossenen Menge in ...n definiert sind.
From isotonic Banach functionals to coherent risk measures
Coherent risk measures [ADEH], introduced to study both market and nonmarket risks, have four characteristic properties that lead to the term “coherent” present in their name. Coherent risk measures regarded as functionals on the space have been extensively studied [De] with respect to these four properties. In this paper we introduce CRM functionals, defined as isotonic Banach functionals [Al], and use them to characterize coherent risk measures on the space as order opposites of CRM functionals....
Generalized-lush spaces and the Mazur-Ulam property
We introduce a new class of Banach spaces, called generalized-lush spaces (GL-spaces for short), which contains almost-CL-spaces, separable lush spaces (in particular, separable C-rich subspaces of C(K)), and even the two-dimensional space with hexagonal norm. We find that the space C(K,E) of vector-valued continuous functions is a GL-space whenever E is, and show that the set of GL-spaces is stable under c₀-, l₁- and -sums. As an application, we prove that the Mazur-Ulam property holds for a larger...
Hahn-Banach theorem implies Riesz theorem.
Ideals of extendable and liftable operators.
Se introducen los ideales de operadores que admiten extensión o levantamiento y se presenta una nueva aproximación al estudio de la escisión de sucesiones exactas cortas de espacios de Banach. Se considera la maximalidad de estos ideales y se investiga si son cerrados respecto de los límites puntuales acotados. Se resumen algunos ejemplos y se clarifica el papel de los espacios L1 y L∞.
Interpolating bases for spaces of differentiable functions
Lifting-Probleme für Vektorfunktionen und ...-Sequenzen.
Locally convex topologies in linear orthogonality spaces
In this paper, we investigate the existence and characterizations of locally convex topologies in a linear orthogonality space.
Mazur-Orlicz equality
A remarkable theorem of Mazur and Orlicz which generalizes the Hahn-Banach theorem is here put in a convenient form through an equality which will be referred to as the Mazur-Orlicz equality. Applications of the Mazur-Orlicz equality to lower barycenters for means, separation principles, Lax-Milgram lemma in reflexive Banach spaces, and monotone variational inequalities are provided.
Nonlinear metric projections in twisted twilight.
Note on Köthe Spaces.
Observación sobre los teoremas de tipo Hahn-Banach.
On basic Hahn-Banach extensions
On extending and lifting continuous linear mappings in topological vector spaces
On extensions of uniformly continuous Banach-space-valued mappings
On holomorphic Hahn-Banach extension theorem and properties of bounding and weakly-bounding sets in some metric vector spaces
On problems concerning extension of linear operations on linear spaces
On separation theorems for subadditive and superadditive functionals
We generalize the well known separation theorems for subadditive and superadditive functionals to some classes of not necessarily Abelian semigroups. We also consider the problem of supporting subadditive functionals by additive ones in the not necessarily commutative case. Our results are motivated by similar extensions of the Hyers stability theorem for the Cauchy functional equation. In this context the so-called weakly commutative and amenable semigroups appear naturally. The relations between...
On Simons' version of Hahn-Banach-Lagrange theorem
In this paper we generalize in Theorem 12 some version of Hahn-Banach Theorem which was obtained by Simons. We also present short proofs of Mazur and Mazur-Orlicz Theorem (Theorems 2 and 3).