-Runge domains for P-holomorphy types
Vengono studiati i legami fra i domini di Runge e domini di Runge di tipo 0 in uno spazio di Banach complesso, introducendo una nuova nozione di dominio di Runge.
Theorems of the Cartan-Thullen Type and -envelope of Holomorphy for Every Holomorphy Type
Dopo aver enunciato alcuni teoremi di tipo Cartan-Thullen sugli aperti c-olomorficamente convessi e cb-olomorficamente convessi, si costruiscono i -inviluppi di olomorfia per ogni tipo di olornorfia .
Holomorphic functions on strict inductive limits of Banach spaces.
In this article we show that a number of apparently different properties coincide on the set of holomorphic functions on a strict inductive limit (all inductive limits are assumed to be countable and proper) of Banach spaces and that they are all satisfied only in the trivial case of a strict inductive limit of finite dimensional spaces. Thus the linear properties of a strict inductive limit of Banach spaces rarely translate themselves into holomorphic properties.
Factorization of uniformly holomorphic functions
Let E be a complex Hausdorff locally convex space such that the strong dual E’ of E is sequentially complete, let F be a closed linear subspace of E and let U be a uniformly open subset of E. We denote by Π: E → E/F the canonical quotient mapping. In §1 we study the factorization of uniformly holomorphic functions through π. In §2 we study F-quotients of uniform type and introduce the concept of envelope of uF-holomorphy of a connected uniformly open subset U of E. The main result states that the...
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