Corrigenda to: "Optimal domains for the kernel operator associated with Sobolev's inequality" (Studia Math. 158 (2003), 131-152)
Decomposition of group-valued additive set functions
Let be an additive function on a ring of sets, with values in a commutative Hausdorff topological group, and let be an ideal of . Conditions are given under which can be represented as the sum of two additive functions, one essentially supported on , the other vanishing on . The result is used to obtain two Lebesgue-type decomposition theorems. Other applications and the corresponding theory for outer measures are also indicated.
Decompositions of set functions
Denseness and Borel complexity of some sets of vector measures
Let ν be a positive measure on a σ-algebra Σ of subsets of some set and let X be a Banach space. Denote by ca(Σ,X) the Banach space of X-valued measures on Σ, equipped with the uniform norm, and by ca(Σ,ν,X) its closed subspace consisting of those measures which vanish at every ν-null set. We are concerned with the subsets and of ca(Σ,X) defined by the conditions |φ| = ν and |φ| ≥ ν, respectively, where |φ| stands for the variation of φ ∈ ca(Σ,X). We establish necessary and sufficient conditions...
Der Satz von Dunford-Pettis und die Darstellung von Massen mit Werten in lokalkonvexen Räumen.
Derivability, variation and range of a vector measure
We prove that the range of a vector measure determines the σ-finiteness of its variation and the derivability of the measure. Let F and G be two countably additive measures with values in a Banach space such that the closed convex hull of the range of F is a translate of the closed convex hull of the range of G; then F has a σ-finite variation if and only if G does, and F has a Bochner derivative with respect to its variation if and only if G does. This complements a result of [Ro] where we proved...
Derivación de medidas e integración vectorial bilineal.
Dérivation de mesures à valeurs vectorielles
Diferenciación de medidas vectoriales en semi-μ-espacios de Lusin.
Dilation theorems for completely positive maps and map-valued measures
The Stinespring theorem is reformulated in terms of conditional expectations in a von Neumann algebra. A generalisation for map-valued measures is obtained.
El teorema de Radon-Nikodym en espacios bornológicos.
Embedding in
If is a measurable space and a Banach space, we provide sufficient conditions on and in order to guarantee that , the Banach space of all -valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of if and only if does.
Errata : « Les semi-martingales formelles »
Espacios LP y teoremas de convergencia para integrales vectoriales.
Estimates of L p norms for sums of positive functions
We present new inequalities of Lp norms for sums of positive functions. These inequalities are useful for investigation of convergence of simple partial fractions in Lp(ℝ).
Exhaustive measures in arbitrary topological vector spaces
Extension of vector measures
Extension theorems (vector measures on quantum logics)
Extensions of additive mappings
Factorization through Hilbert space and the dilation of L(X,Y)-valued measures
We present a general necessary and sufficient algebraic condition for the spectral dilation of a finitely additive L(X,Y)-valued measure of finite semivariation when X and Y are Banach spaces. Using our condition we derive the main results of Rosenberg, Makagon and Salehi, and Miamee without the assumption that X and/or Y are Hilbert spaces. In addition we relate the dilation problem to the problem of factoring a family of operators through a single Hilbert space.