Extendability and domains of holomorphy in infinite-dimensional spaces
Volume 123 / 2019
Annales Polonici Mathematici 123 (2019), 31-41
MSC: Primary 46G20; Secondary 58B12.
DOI: 10.4064/ap180821-5-12
Published online: 12 April 2019
Abstract
We study the notions of extendability and domain of holomorphy in the infinite-dimensional case. In this setting it is also true that the notions of domain of holomorphy and weak domain of holomorphy are equivalent. We also prove that the set of non-extendable functions belonging to some classes $X(B)\subset H(B)$, $B$ being the open unit ball in a separable complex Banach space, is a lineable and dense $G_\delta .$ Moreover, when $\varOmega $ is $H_b$-holomorphically convex (defined in the text), it is shown that the set of non-extendable holomorphic functions on $\varOmega $ is a lineable and dense $G_\delta $ set.
