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THE BOUNDED APPROXIMATION PROPERTY FOR THE WEIGHTED SPACES OF HOLOMORPHIC MAPPINGS ON BANACH SPACES.
- Source :
- Glasgow Mathematical Journal; May2018, Vol. 60 Issue 2, p307-320, 14p
- Publication Year :
- 2018
-
Abstract
- In this paper, we study the bounded approximation property for the weighted space $\mathcal{HV}$(U) of holomorphic mappings defined on a balanced open subset U of a Banach space E and its predual $\mathcal{GV}$(U), where $\mathcal{V}$ is a countable family of weights. After obtaining an $\mathcal{S}$-absolute decomposition for the space $\mathcal{GV}$(U), we show that E has the bounded approximation property if and only if $\mathcal{GV}$(U) has. In case $\mathcal{V}$ consists of a single weight v, an analogous characterization for the metric approximation property for a Banach space E has been obtained in terms of the metric approximation property for the space $\mathcal{G}_v$(U). [ABSTRACT FROM PUBLISHER]
- Subjects :
- BANACH spaces
APPROXIMATION theory
SUBSET selection
SET theory
MATHEMATICAL mappings
Subjects
Details
- Language :
- English
- ISSN :
- 00170895
- Volume :
- 60
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Glasgow Mathematical Journal
- Publication Type :
- Academic Journal
- Accession number :
- 128976213
- Full Text :
- https://doi.org/10.1017/S0017089517000118