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THE BOUNDED APPROXIMATION PROPERTY FOR THE WEIGHTED SPACES OF HOLOMORPHIC MAPPINGS ON BANACH SPACES

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).

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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