Non-separable tree-like Banach spaces and Rosenthal's ℓ₁-theorem

الأصل · EN

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