VECTOR SPACES OF ENTIRE FUNCTIONS OF UNBOUNDED TYPE

被引：12
|
作者：
Lopez-Salazar Codes, Jeronimo [1 ]
机构：
[1] Univ Complutense Madrid, Dept Anal Matemat, E-28040 Madrid, Spain
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2011年 / 139卷 / 04期
关键词：
Entire function; lineable set; tau delta topology; BANACH-SPACES;
D O I：
10.1090/S0002-9939-2010-10817-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let E be an infinite dimensional complex Banach space. We prove the existence of an infinitely generated algebra, an infinite dimensional closed subspace and a dense subspace of entire functions on E whose non-zero elements are functions of unbounded type. We also show that the tau delta topology on the space of all holomorphic functions cannot be obtained as a countable inductive limit of Frechet spaces.
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页码：1347 / 1360
页数：14
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