Abstract
James Tree Space (JT), introduced by R. James in James (1974), is the first Banach space constructed having non-separable conjugate and not containing ℓ1. James actually proved that every infinite dimensional subspace of JT contains a Hilbert space, which implies the ℓ1 non-embedding. In this expository article, we present a direct proof of the ℓ1 non-embedding, using Rosenthal’s ℓ1-Theorem (Rosenthal, 1974) and some measure theoretic arguments, namely Riesz’s Representation Theorem (Rudin, 1966).
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