Abstract
Letτ be a cardinal with cf(τ)>ℵ0. Then a Banach spaceE contains a subspace isomorphic tol l(τ) if and only if [0,1]r is a continuous image of the unit ballE′1 ofE′, provided with the w*-topology. It follows that, for each cardinalκ, ifE′1 contains a copy ofβκ, thenE has a quotient isomorphic tol ∞(κ). In this situation we show thatE has even a quotientisometric tol ∞(κ).
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Talagrand, M. Sur les espaces de Banach contenantl 1(τ). Israel J. Math. 40, 324–330 (1981). https://doi.org/10.1007/BF02761372
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DOI: https://doi.org/10.1007/BF02761372