Non-separable tree-like Banach spaces and Rosenthal's ℓ₁-theorem
Costas Poulios (2014)
Studia Mathematica
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We introduce and investigate a class of non-separable tree-like Banach spaces. As a consequence, we prove that we cannot achieve a satisfactory extension of Rosenthal's ℓ₁-theorem to spaces of the type ℓ₁(κ) for κ an uncountable cardinal.