A general separation theorem for mappings, saddle-points duality and conjugate functions
A generalisation of a theorem of Koldunov with an elementary proof
We generalize a Theorem of Koldunov [2] and prove that a disjointness proserving quasi-linear operator between Resz spaces has the Hammerstein property.
A generalization of Dragilev's theorem.
A Generalization of Echelon Spaces.
A generalization of the Hahn-Banach theorem
If C is a non-empty convex subset of a real linear space E, p: E → ℝ is a sublinear function and f:C → ℝ is concave and such that f ≤ p on C, then there exists a linear function g:E → ℝ such that g ≤ p on E and f ≤ g on C. In this result of Hirano, Komiya and Takahashi we replace the sublinearity of p by convexity.
A generalization of the Nikodym boundedness theorem.
In this note an internal property of a ring of sets, named the Nested Partition Property, is shown to imply the Nikodym Property. A wide range of examples are shown to have this property.
A generalization of Yano's extrapolation theorem
A generalized mixed topology on Orlicz spaces.
A Geometrical Characterization of Choquet Simplexes.
A Grothendieck Representation for the Completion of Cones of Continuous Seminorms.
A Hahn-Banach Theorem for Holomorphic Mappings on Locally Convex Spaces.
A Hahn-Banach theorem for separation of semigroups and its application.
A Hahn-Banach Theorem in Conjugate Banach Spaces.
A Hahn-Banach type generalization of the Hyers-Ulam theorem.
A hereditary property in locally convex spaces
If is an infrabarrelled space, it is proved that any subspace , of finite codimension, is infrabarrelled.
A "hidden" characterization of approximatively polyhedral convex sets in Banach spaces
A closed convex subset C of a Banach space X is called approximatively polyhedral if for each ε > 0 there is a polyhedral (= intersection of finitely many closed half-spaces) convex set P ⊂ X at Hausdorff distance < ε from C. We characterize approximatively polyhedral convex sets in Banach spaces and apply the characterization to show that a connected component of the space of closed convex subsets of X endowed with the Hausdorff metric is separable if and only if contains a polyhedral convex...
A "hidden" characterization of polyhedral convex sets
We prove that a closed convex subset C of a complete linear metric space X is polyhedral in its closed linear hull if and only if no infinite subset A ⊂ X∖ C can be hidden behind C in the sense that [x,y]∩ C ≠ ∅ for any distinct x,y ∈ A.
A Lagrange multiplier theorem and a sandwich theorem for convex relations.
A Large Bi-Invariant Nuclear Function Space on a Locally Compact Group.
A Leray--Schauder alternative for weakly-strongly sequentially continuous weakly compact maps.