The Zorn property for holomorphic functions
Volume 120 / 2017
Annales Polonici Mathematici 120 (2017), 115-133
MSC: 32A10, 46A04, 46E50, 46G20, 46A63.
DOI: 10.4064/ap170707-11-11
Published online: 4 December 2017
Abstract
The aim of this paper is to investigate Zorn’s property for the space $(E_B, \tau _E)$, where $E_B$ the linear hull of some compact, absolutely convex subset $B$ of a Fréchet space $E$ and the topology $\tau _E$ on $E_B$ is induced by the topology of $E.$ Furthermore, holomorphic extensions from $(E_B, \tau _E)$ are considered. Based on these results, we establish some results on extension of a Fréchet-valued continuous function $f$ to an entire function from a non-polar balanced convex compact subset $B$ of a Fréchet space whenever $f$ is approximated fast enough on $B$ by a sequence of polynomials.
