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

  • Spiros A. Argyros (a1) and Athanasios Tsarpalias (a1)

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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.

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(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).
(2)Argyros, S. and Tsarpalias, A.Calibers on compact spaces. Trans. A.M.S. 270 (1982), 149162.
(3)Argyros, S.Boolean Algebras without free families. Alg. Universalis 14 (1982), 244256.
(4)Argyros, S.On compact spaces without strictly positive measure. Pacific J. Math. (to appear).
(5)Comfort, W. W. and Negrepontis, S.The theory of ultrafdters, Band 211 (Springer Verlag, 1974).
(6)Hagler, J.On the structure S and C(S) for S dyadic. Trans. A.M.S. 214 (1975), 415417.
(7)Haydon, R.On Banach spaces which contain l 1(T) and types of measures on compact spaces. Israel J. Math. 28 (1977), 313324.
(8)Haydon, R.On dual L 1 spaces and injective bidual Banach spaces. Israel J. Math. 7 (1978), 142152.
(9)Pelczynski, A.Projections in certain B-spaces. Studia Math. 19 (1960), 209228.
(10)Rosenthal, H. P.On injective B-spaces and the spaces L (µ) for finite measure µ. Acta Math. (1970), 205248.
(11)Rosenthal, H. P.On relatively disjoint families of measures with some applications to Banach space theory. Studia Math. 37 (1970), 1336.
(12)Rosenthal, H. P.A characterisation of Banach spaces containing l 1. Proc. Nat. Acad. Sci. U.S.A. 71 (1975), 415417.
(13)Talagrand, M.Sur les espaces de Banach contenant l 1(r). Israel J. Math. 40 (1981), 329330.

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

  • Spiros A. Argyros (a1) and Athanasios Tsarpalias (a1)

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