Smooth measures, the Malliavin calculus and approximations in infinitedimensional spaces
Smooth partitions of unity in preduals of WCG spaces.
Smoothness in Banach spaces. Selected problems.
This is a short survey on some recent as well as classical results and open problems in smoothness and renormings of Banach spaces. Applications in general topology and nonlinear analysis are considered. A few new results and new proofs are included. An effort has been made that a young researcher may enjoy going through it without any special pre-requisites and get a feeling about this area of Banach space theory. Many open problems of different level of difficulty are discussed. For the reader...
Smoothness of a typical convex function
Sobolev type inequalities for p>0
Sobolev's and local derivatives
Sobre el teorema de Dieudonné-Cirothendieck.
Sobre el teorema de Dieudonné-Grothendieck. Condiciones necesarias y suficientes.
Sobre la derivabilidad del producto de medidas vectoriales.
Sobre la existencia del producto de medidas valoradas en espacios localmente convexos: una condición necesaria.
A necessary condition is given for the existence of the tensor product of certain measures valued in locally convex spaces.
Some applications of projective tensor products to holomorphy.
Some change of variable formulas in integral representation theory.
Some convergence theorems for HK-integral in locally convex spaces
We present some convergence theorems for the HK-integral of functions taking values in a locally convex space. These theorems are based on the concept of HK-equiintegrability.
Some convexity questions arising in statistical mechanics.
Some integral representations of differentiable functions.
Some more recent results concerning weak Asplund spaces.
Some new classes of Banach-Mackey spaces.
Some problems arising in connection with the theory of vector measures
Some problems for measures on non-standard algebraic structures
Nell'ultimo ventennio tutta una serie di lavori è stata rivolta allo studio delle misure su strutture algebriche più generali delle algebre di Boole, come i poset e i reticoli ortomodulari, le effect algebras, le BCK-algebras. La teoria così ottenuta interessa l'analisi funzionale, il calcolo delle probabilità e la topologia, più recentemente la teoria delle decisioni. Si presentano alcuni risultati relativi a misure su strutture algebriche non-standard analizzando, in particolare, gli aspetti topologici...
Some properties and applications of equicompact sets of operators
Let X and Y be Banach spaces. A subset M of (X,Y) (the vector space of all compact operators from X into Y endowed with the operator norm) is said to be equicompact if every bounded sequence (xₙ) in X has a subsequence such that is uniformly convergent for T ∈ M. We study the relationship between this concept and the notion of uniformly completely continuous set and give some applications. Among other results, we obtain a generalization of the classical Ascoli theorem and a compactness criterion...