Characterization for relations on some summability methods.
In this paper we obtain two new characterizations of completeness of a normed space through the behaviour of its weakly unconditionally Cauchy series. We also prove that barrelledness of a normed space can be characterized through the behaviour of its weakly- unconditionally Cauchy series in .
Notre étude porte sur une catégorie de structures de Poisson singulières holomorphes au voisinage de et admettant une forme normale formelle polynomiale i.e. un nombre fini d’invariants formels. Les séries normalisantes sont divergentes en général. On montre l’existence de transformations normalisantes holomorphes sur des domaines sectoriels de la forme , où est un monôme associé au problème. Il suit une classification analytique.
Kechris and Louveau in [5] classified the bounded Baire-1 functions, which are defined on a compact metric space , to the subclasses , . In [8], for every ordinal we define a new type of convergence for sequences of real-valued functions (-uniformly pointwise) which is between uniform and pointwise convergence. In this paper using this type of convergence we obtain a classification of pointwise convergent sequences of continuous real-valued functions defined on a compact metric space , and...
Let a be a sequence of points in the unit ball of Cn. Eric Amar and the author have introduced the nonnegative quantity ρ(a) = infα infk Πj:j≠k dG(αj, αk), where dG is the Gleason distance in the unit disk and the first infimum is taken over all sequences α in the unit disk which map to a by a map from the disk to the ball.The value of ρ(a) is related to whether a is an interpolating sequence with respect to analytic disks passing through it, and if a is an interpolating sequence in the ball, then...