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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

REFERENCES

(1)Argyros, S. and Negrepontis, S.Universal embeddings of l1α into C(X) and L ∞ (µ). Colloq. Math. Soc. (Janos Bolyai Topology (23), Budapest, 1978).Google Scholar
(2)Argyros, S. and Tsarpalias, A.Calibers on compact spaces. Trans. A.M.S. 270 (1982), 149–162.CrossRefGoogle Scholar
(3)Argyros, S.Boolean Algebras without free families. Alg. Universalis 14 (1982), 244–256.CrossRefGoogle Scholar
(4)Argyros, S.On compact spaces without strictly positive measure. Pacific J. Math. (to appear).Google Scholar
(5)Comfort, W. W. and Negrepontis, S.The theory of ultrafdters, Band 211 (Springer Verlag, 1974).CrossRefGoogle Scholar
(6)Hagler, J.On the structure S and C(S) for S dyadic. Trans. A.M.S. 214 (1975), 415–417.Google Scholar
(7)Haydon, R.On Banach spaces which contain l 1(T) and types of measures on compact spaces. Israel J. Math. 28 (1977), 313–324.CrossRefGoogle Scholar
(8)Haydon, R.On dual L 1 spaces and injective bidual Banach spaces. Israel J. Math. 7 (1978), 142–152.CrossRefGoogle Scholar
(9)Pelczynski, A.Projections in certain B-spaces. Studia Math. 19 (1960), 209–228.CrossRefGoogle Scholar
(10)Rosenthal, H. P.On injective B-spaces and the spaces L ∞(µ) for finite measure µ. Acta Math. (1970), 205–248.CrossRefGoogle Scholar
(11)Rosenthal, H. P.On relatively disjoint families of measures with some applications to Banach space theory. Studia Math. 37 (1970), 13–36.CrossRefGoogle Scholar
(12)Rosenthal, H. P.A characterisation of Banach spaces containing l 1. Proc. Nat. Acad. Sci. U.S.A. 71 (1975), 415–417.Google Scholar
(13)Talagrand, M.Sur les espaces de Banach contenant l 1(r). Israel J. Math. 40 (1981), 329–330.CrossRefGoogle Scholar