1Department of Mathematics Quy Nhon University 170 An Duong Vuong Quy Nhon, Binh Dinh, Vietnam 2Department of Mathematics Vinh Phuc College 2 Trung Trac Street Phuc Yen, Vinh Phuc, Vietnam 3Department of Mathematics Thai Nguyen University of Education Luong Ngoc Quyen Street Thai Nguyen City, Vietnam
Annales Polonici Mathematici, Tome 120 (2017) no. 2, pp. 115-133
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.
Keywords:
paper investigate zorn property space tau where linear hull compact absolutely convex subset chet space topology tau induced topology furthermore holomorphic extensions tau considered based these results establish results extension chet valued continuous function entire function non polar balanced convex compact subset chet space whenever approximated fast enough sequence polynomials
Affiliations des auteurs :
Thai Thuan Quang
1
;
Duong Thanh Vy
1
;
Le Thanh Hung
2
;
Pham Hien Bang
3
1
Department of Mathematics Quy Nhon University 170 An Duong Vuong Quy Nhon, Binh Dinh, Vietnam
2
Department of Mathematics Vinh Phuc College 2 Trung Trac Street Phuc Yen, Vinh Phuc, Vietnam
3
Department of Mathematics Thai Nguyen University of Education Luong Ngoc Quyen Street Thai Nguyen City, Vietnam
@article{10_4064_ap170707_11_11,
author = {Thai Thuan Quang and Duong Thanh Vy and Le Thanh Hung and Pham Hien Bang},
title = {The {Zorn} property for holomorphic functions},
journal = {Annales Polonici Mathematici},
pages = {115--133},
year = {2017},
volume = {120},
number = {2},
doi = {10.4064/ap170707-11-11},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap170707-11-11/}
}
TY - JOUR
AU - Thai Thuan Quang
AU - Duong Thanh Vy
AU - Le Thanh Hung
AU - Pham Hien Bang
TI - The Zorn property for holomorphic functions
JO - Annales Polonici Mathematici
PY - 2017
SP - 115
EP - 133
VL - 120
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4064/ap170707-11-11/
DO - 10.4064/ap170707-11-11
LA - en
ID - 10_4064_ap170707_11_11
ER -
%0 Journal Article
%A Thai Thuan Quang
%A Duong Thanh Vy
%A Le Thanh Hung
%A Pham Hien Bang
%T The Zorn property for holomorphic functions
%J Annales Polonici Mathematici
%D 2017
%P 115-133
%V 120
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/ap170707-11-11/
%R 10.4064/ap170707-11-11
%G en
%F 10_4064_ap170707_11_11
Thai Thuan Quang; Duong Thanh Vy; Le Thanh Hung; Pham Hien Bang. The Zorn property for holomorphic functions. Annales Polonici Mathematici, Tome 120 (2017) no. 2, pp. 115-133. doi: 10.4064/ap170707-11-11
