Boundedly complete basic sequences, c 0-subspaces, and injections of Banach spaces

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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 languageEnglish
Pages (from-to)173-188
Number of pages16
JournalIsrael Journal of Mathematics
Volume89
Issue number1-3
DOIs
StatePublished - 1 Oct 1995

ASJC Scopus subject areas

  • Mathematics (all)

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