Factorization of Holomorphic Mappings in Infinite Dimensions.
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...
Factorization of weakly continuous holomorphic mappings
We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly uniformly} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Hervés and Valdivia for polynomials between Banach spaces, and it also holds if the weak topology is replaced by a coarser...
Fixed points and periodic points of semiflows of holomorphic maps.
Fixed points of holomorphic mappings for domains in Banach spaces.
Fixed points of holomorphic mappings in the Hilbert ball
Fonctions analytiques et fonctions plurisousharmoniques dans les espaces vectoriels topologiques
Fréchet-valued analytic functions and linear topological invariants.
Fully summing mappings between Banach spaces
We introduce and investigate the non-n-linear concept of fully summing mappings; if n = 1 this concept coincides with the notion of nonlinear absolutely summing mappings and in this sense this article unifies these two theories. We also introduce a non-n-linear definition of Hilbert-Schmidt mappings and sketch connections between this concept and fully summing mappings.
Functional Banach spaces of holomorphic functions on Reinhardt domains