Holomorphic Functions on Strict Inductive Limits of Banach Spaces

Sin resume

Fredholm-valued holomorphic mappings on a Banach space

AbstractIn this article we show that the pointwise existence of a regulariser for holomorphic Fredhom-valued mappings defined on pseudo-convex domains in Banach spaces with an unconditional basis implies the existence of a holomorphic regulariser

Inverses depending holomorphically on a parameter in a Banach space

AbstractWe show that the existence of a right inverse at each point for a holomorphic mapping from a pseudo-convex domain in a Banach space with an unconditional basis into a unital Banach algebra implies the existence of a holomorphic right inverse. Variations of this result are given

Locally determining sequences in infinite-dimensional spaces.

A subset L of a complex locally convex space E is said to be locally determining at 0 for holomorphic functions if for every connected open 0-neighborhood U and every f∈H(U), whenever f vanishes on U∩L, then f≡0. The authors' main result is that if E is separable and metrizable, then every set which is locally determining at 0 contains a null sequence which is also locally determining at 0. This answers a question of J. Chmielowski [Studia Math. 57 (1976), no. 2, 141–146;], who was the first to study locally determining sets. The proof of the main theorem makes use of the following result of K. F. Ng [Math. Scand. 29 (1971), 279–280;]: Let E be a normed space with closed unit ball BE. Suppose that there is a Hausdorff locally convex topology τ on E such that (BE,τ) is compact. Then E with its original norm is the dual of the normed space F={φ∈E∗: φ|BE is τ-continuous}, with norm ∥φ∥=sup{|φ(x)|: x∈BE

Banach subspaces of spaces of holomorphic functions and related topics

Fil: Dimant, Verónica. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.Fil: Dineen, Seán. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina