## Abstract

We study the connection between topological properties of subsets of a given Banach space and their images under linear, continuous one-to-one mappings on the one hand and the existence in a given Banach space of either a boundedly complete basic sequence (BCBS) or an isomorphic copy of c_{ o} (c_{ o} -subspace) on the other hand. We present criteria for the existence of a BCBS. They are deduced from new characterisations of G_{ δ}-embeddings which we also present. We obtain a necessary and sufficient condition for separability of a dual Banach space in terms of saturation by BCBS. Criteria for the existence in a Banach space of a c_{ o} -subspace are also presented. We describe the class of separable Banach spaces which contains either a BCBS or a c_{ o} -subspace.

Original language | English |
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Pages (from-to) | 173-188 |

Number of pages | 16 |

Journal | Israel Journal of Mathematics |

Volume | 89 |

Issue number | 1-3 |

DOIs | |

State | Published - 1 Oct 1995 |

## ASJC Scopus subject areas

- Mathematics (all)

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