An Orlicz-Pettis type property for vector measures and also the “Uniform Boundedness Principle” are shown to fail without local convexity assumption. The author asks under which generalized convexity hypotheses these properties remain true. This problem is expressed in terms of barrelledness type conditions.
We study a quantum extension of the Lévy Laplacian, so-called quantum Lévy-type Laplacian, to the nuclear algebra of operators on spaces of entire functions. We give several examples of the action of the quantum Lévy-type Laplacian on basic operators and we study a quantum white noise convolution differential equation involving the quantum Lévy-type Laplacian.
Sia uno spazio riflessivo e sia un compatto di . Si dimostra che lo spazio dei germi olomorfi su , con la topologia naturale, è un limite induttivo regolare e quasi completo purché lo spazio dei germi olomorfi all'origine sia un limite induttivo regolare.
A class of locally convex vector spaces with a special Schauder decomposition is considered. It is proved that the elements of this class, which includes some spaces naturally appearing in infinite dimensional holomorphy, are quasinormable though in general they are neither metrizable nor Schwartz spaces.
Nous donnons des conditions permettant de vérifier que l’image d’une mesure cylindrique sur un espace vectoriel topologique , par une application linéaire continue dans un autre espace vectoriel topologique , est une mesure de Randon. Dans une première partie, nous donnons des résultats généraux qui portent, soit sur des propriétés géométriques de l’espace , soit sur la mesure cylindrique . Dans une seconde partie, nous donnons des conditions plus précises quand est une mesure cylindrique...
The main concern of this paper is to present some improvements to results on the existence or non-existence of countably additive Borel measures that are not Radon measures on Banach spaces taken with their weak topologies, on the standard axioms (ZFC) of set-theory. However, to put the results in perspective we shall need to say something about consistency results concerning measurable cardinals.
For a Banach space and a probability space , a new proof is given that a measure , with , has RN derivative with respect to iff there is a compact or a weakly compact such that is a finite valued countably additive measure. Here we define where is a finite disjoint collection of elements from , each contained in , and satisfies . Then the result is extended to the case when is a Frechet space.
It is proved that if a Frechet space has property, then also has property, for .