A KSGNS (Kasparov, Stinespring, Gel'fand, Naimark, Segal) type construction for strict (respectively, covariant non-degenerate) completely multi-positive linear maps between locally C*-algebras is described.
We look at normed spaces of differentiable functions on compact plane sets, including the spaces of infinitely differentiable functions considered by Dales and Davie in [7]. For many compact plane sets the classical definitions give rise to incomplete spaces. We introduce an alternative definition of differentiability which allows us to describe the completions of these spaces. We also consider some associated problems of polynomial and rational approximation.
Soit une suite de Blaschke du disque unité et une fonction intérieure. On suppose que la suite de noyaux reproduisants est complète dans l’espace modèle , . On étudie, dans un premier temps, la stabilité de cette propriété de complétude, à la fois sous l’effet de perturbations des fréquences mais également sous l’effet de perturbations de la fonction . On retrouve ainsi un certain nombre de résultats classiques sur les systèmes d’exponentielles. Puis, si on suppose de plus que la suite ...
We study the classes of complex Banach spaces with Valdivia dual unit ball. We give complex analogues of several theorems on real spaces. Further we study relationship of these complex Banach spaces with their real versions and that of real Banach spaces and their complexification. We also formulate several open problems.