The range of vector measures into Orlicz spaces
The Sobolev spaces of harmonic functions
The (sub/super)additivity assertion of Choquet
The assertion in question comes from the short final section in Theory of capacities of Choquet (1953/54), in connection with his prototype of the subsequent Choquet integral. The problem was whether and when this operation is additive. Choquet had the much more abstract idea that all functionals in a certain wide class must be subadditive, and similarly for superadditivity. His treatment of this point was more like an outline, and his proof limited to a rather narrow special case. Thus the proper...
The symmetric Choquet integral with respect to Riesz-space-valued capacities
A definition of “Šipoš integral” is given, similarly to [3],[5],[10], for real-valued functions and with respect to Dedekind complete Riesz-space-valued “capacities”. A comparison of Choquet and Šipoš-type integrals is given, and some fundamental properties and some convergence theorems for the Šipoš integral are proved.
The symmetric tensor product of a direct sum of locally convex spaces
An explicit representation of the n-fold symmetric tensor product (equipped with a natural topology τ such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for gives a direct proof of a recent result of Díaz and Dineen (and generalizes it to other topologies τ) that the n-fold projective symmetric and the n-fold projective “full” tensor product of a locally convex space E are isomorphic if E is isomorphic to its square .
The theorems of Glicksberg and Hurwitz for holomorphic maps in complex Banach spaces
General versions of Glicksberg's theorem concerning zeros of holomorphic maps and of Hurwitz's theorem on sequences of analytic functions is extended to infinite dimensional Banach spaces.
The theory of bounding subsets of topological vector spaces without convexity condition
The theory of stationary vector-valued measures over R.
The topological complexity of sets of convex differentiable functions.
Let C(X) be the set of all convex and continuous functions on a separable infinite dimensional Banach space X, equipped with the topology of uniform convergence on bounded subsets of X. We show that the subset of all convex Fréchet-differentiable functions on X, and the subset of all (not necessarily equivalent) Fréchet-differentiable norms on X, reduce every coanalytic set, in particular they are not Borel-sets.
The Vitali convergence theorem for the vector-valued McShane integral
The classical Vitali convergence theorem gives necessary and sufficient conditions for norm convergence in the space of Lebesgue integrable functions. Although there are versions of the Vitali convergence theorem for the vector valued McShane and Pettis integrals given by Fremlin and Mendoza, these results do not involve norm convergence in the respective spaces. There is a version of the Vitali convergence theorem for scalar valued functions defined on compact intervals in given by Kurzweil and...
The weak McShane integral
We present a weaker version of the Fremlin generalized McShane integral (1995) for functions defined on a -finite outer regular quasi Radon measure space into a Banach space and study its relation with the Pettis integral. In accordance with this new method of integration, the resulting integral can be expressed as a limit of McShane sums with respect to the weak topology. It is shown that a function from into is weakly McShane integrable on each measurable subset of if and only if...
The weak Radon-Nikodym property
The weak Radon-Nikodym property in Banach spaces
The -function in the space .
Théorème de relèvement et mesures bivalentes
Théorème de relèvement et mesures bivalentes
Théorèmes de factorisation pour les opérateurs à valeurs dans un espace
Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans un espace
Théorèmes d'identité en dimension infinie
Theory of Fréchet cones