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

GUPTA, MANJUL ; BAWEJA, DEEPIKA

Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 307-320

Résumé

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).

Détail

DOI : 10.1017/S0017089517000118

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