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Isomorphic embeddings of l1(Г) into subspaces of C(Ω)*

Published online by Cambridge University Press:  24 October 2008

Spiros A. Argyros  and
Athanasios Tsarpalias
Spiros A. Argyros
Affiliation:
Athens University
Athanasios Tsarpalias
Affiliation:
Athens University
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Extract

Introduction. The embeddability of l1(Γ), for uncountable sets Γ, into subspaces of Banach spaces of the form C(Ω) was investigated first by Hagler in (6) and subsequently by Haydon in (7), (8) and Argyros and Negrepontis in (1). An important role in the development of the above subject is played by a lemma of Rosenthal (12) that translates the functional analytic problem of finding a family {fξ: ξ Γ} of elements of C(Ω) equivalent to the usual basis of l1(Γ) into the problem of the existence of an independent family {(Aξ, Bξ,): ξ є Γ} of closed subsets.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 2 , September 1982 , pp. 251 - 262
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

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