p-convex functions in linear spaces
Plurisubharmonic functions on compact sets
Poletsky has introduced a notion of plurisubharmonicity for functions defined on compact sets in ℂⁿ. We show that these functions can be completely characterized in terms of monotone convergence of plurisubharmonic functions defined on neighborhoods of the compact.
Points fixes des contractions de certains faiblement compacts de
Positive linear maps of matrix algebras
A characterization of the structure of positive maps is presented. This sheds some more light on the old open problem studied both in Quantum Information and Operator Algebras. Our arguments are based on the concept of exposed points, links between tensor products and mapping spaces and convex analysis.
Problème des moments -dimensionnel ; mesures quasi-spectrales et semi-groupes
Products and projective limits of function spaces
We introduce a notion of a product and projective limit of function spaces. We show that the Choquet boundary of the product space is the product of Choquet boundaries. Next we show that the product of simplicial spaces is simplicial. We also show that the maximal measures on the product space are exactly those with maximal projections. We show similar characterizations of the Choquet boundary and the space of maximal measures for the projective limit of function spaces under some additional assumptions...
Propriétés géométriques des sous-espaces invariants par translation de et
(P)-sets, quasipolyhedra and stability
Pseudo-boundaries and pseudo-interiors for topological convexities [Book]
Quelques remarques sur la propriété (C) des espaces de Banach
Quelques résultats nouveaux sur les points extrémaux d'un simplexe compact
Recognizing the topology of the space of closed convex subsets of a Banach space
Relative Commutants in Compact Convex Sets and Banach Spaces.
Remark on the Abstract Dirichlet Problem for Baire-One Functions
We study the possibility of extending any bounded Baire-one function on the set of extreme points of a compact convex set to an affine Baire-one function and related questions. We give complete solutions to these questions within a class of Choquet simplices introduced by P. J. Stacey (1979). In particular we get an example of a Choquet simplex such that its set of extreme points is not Borel but any bounded Baire-one function on the set of extreme points can be extended to an affine Baire-one function....
Remarks on delta-convex functions
Remarks on weakly KKM maps in abstract convex spaces.
Renorming Concerning Mazur's Intersection Property of Balls for Weakly Compact Convex Sets.
Représentation des mesures coniques.
Représentations intégrales dans les cônes convexes conucléaires et applications
Rotundity and smoothness of convex bodies in reflexive and nonreflexive spaces
For combining two convex bodies C and D to produce a third body, two of the most important ways are the operation ∓ of forming the closure of the vector sum C+D and the operation γ̅ of forming the closure of the convex hull of C ⋃ D. When the containing normed linear space X is reflexive, it follows from weak compactness that the vector sum and the convex hull are already closed, and from this it follows that the class of all rotund bodies in X is stable with respect to the operation ∓ and the class...