p-integrale selectors of multimeasures.
Points fixes et théorèmes ergodiques dans les espaces L¹(E)
We prove that for each linear contraction T : X → X (∥T∥ ≤ 1), the subspace F = {x ∈ X : Tx = x} of fixed points is 1-complemented, where X is a suitable subspace of L¹(E*) and E* is a separable dual space such that the weak and weak* topologies coincide on the unit sphere. We also prove some related fixed point results.
Pointwise compactness and continuity of the integral.
In this paper we bring together the different known ways of establishing the continuity of the integral over a uniformly integrable set of functions endowed with the topology of pointwise convergence. We use these techniques to study Pettis integrability, as well as compactness in C(K) spaces endowed with the topology of pointwise convergence on a dense subset D in K.
Pointwise Compactness and Weakly Compact Sets in L...
Positive operator bimeasures and a noncommutative generalization
For C*-algebras A and B and a Hilbert space H, a class of bilinear maps Φ: A× B → L(H), analogous to completely positive linear maps, is studied. A Stinespring type representation theorem is proved, and in case A and B are commutative, the class is shown to coincide with that of positive bilinear maps. As an application, the extendibility of a positive operator bimeasure to a positive operator measure is shown to be equivalent to various conditions involving positive scalar bimeasures, pairs of...
Positive vector measures with given marginals
Suppose is an ordered locally convex space, and Hausdorff completely regular spaces and a uniformly bounded, convex and closed subset of . For , let . Then, under some topological and order conditions on , necessary and sufficient conditions are established for the existence of an element in , having marginals and .
Product of dominated vector measures
Products and convolutions of vector valued set functions
Products of group-valued measures
Products of Vector Measures
Products of vector measures by means of Fubini's theorem
Projective limits of vector measures.
A necessary and sufficient condition for the existence of the projective limit of measures with values in a locally convex space is given. A similar theorem for measures with values in different locally convex spaces (under certain conditions) is given too (in this case, the projective limit is valued in the projective limit of these spaces). Finally, a result about the projective limit of vector measures is stated.
Projective Tensor Product of -Valued Measures
Prolungamenti simultanei di misure
Property and the reciprocal Dunford-Pettis property in projective tensor products
A Banach space has the reciprocal Dunford-Pettis property () if every completely continuous operator from to any Banach space is weakly compact. A Banach space has the (resp. property ) if every -subset of is relatively weakly compact (resp. weakly precompact). We prove that the projective tensor product has property when has the , has property , and .
Proprites de Radon-Nikodym pour les cones positifs de mesures.