The bounded approximation property for spaces of holomorphic mappings on infinite dimensional spaces

被引：5
作者：
Caliskan, Erhan [1 ]
机构：
[1] Yildiz Tek Univ, Davutpasa Yerlesim Birimi, Fen Edebiyat Fak, Matemat Bolumu, Istanbul, Turkey
来源：
MATHEMATISCHE NACHRICHTEN | 2006年 / 279卷 / 07期
关键词：
approximation property; bounded approximation property; holomorphic mappings; germs of holomorphic functions;
D O I：
10.1002/mana.200310387
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the bounded approximation property for spaces of holomorphic functions. We show that if U is a balanced open subset of a Frechet-Schwartz space or (DFM)-space E, then the space R(U) of holomorphic mappings on U, with the compact-open topology, has the bounded approximation property if and only if E has the bounded approximation property.
引用
收藏
页码：705 / 715
页数：11
相关论文
共 29 条
[1]   ON A PROBLEM OF TOPOLOGIES IN INFINITE DIMENSIONAL HOLOMORPHY [J].
ANSEMIL, JM ;
TASKINEN, J .
ARCHIV DER MATHEMATIK, 1990, 54 (01) :61-64
[2]   COMPACT HOLOMORPHIC MAPPINGS ON BANACH-SPACES AND APPROXIMATION PROPERTY [J].
ARON, RM ;
SCHOTTENLOHER, M .
JOURNAL OF FUNCTIONAL ANALYSIS, 1976, 21 (01) :7-30
[3]  
Bierstedt K.D., 1988, Functional Analysis and its Applications, P35
[4]  
BIERSTEDT KD, 1996, FUNCTIONAL ANAL, P35
[5]   MONTEL AND REFLEXIVE PREDUALS OF SPACES OF HOLOMORPHIC-FUNCTIONS ON FRECHET SPACES [J].
BOYD, C .
STUDIA MATHEMATICA, 1993, 107 (03) :305-315
[6]   Weakly uniformly continuous holomorphic functions and the approximation property [J].
Boyd, C ;
Dineen, S ;
Rueda, P .
INDAGATIONES MATHEMATICAE-NEW SERIES, 2001, 12 (02) :147-156
[7]  
Boyd C, 1994, P ROY IRISH ACAD A, V94A, P167
[8]  
BOYD C, 1993, REV MAT COMPLUT, V6, P221
[9]  
Casazza PG, 2001, HANDBOOK OF THE GEOMETRY OF BANACH SPACES, VOL 1, P271, DOI 10.1016/S1874-5849(01)80009-7
[10]   The approximation property for spaces of holomorphic functions on infinite-dimensional spaces I [J].
Dineen, S ;
Mujica, J .
JOURNAL OF APPROXIMATION THEORY, 2004, 126 (02) :141-156
123