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Register a new userOn the non-embedding of $ell_1$ in the James Tree Space
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Authors
Ioakeim Ampatzoglou
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James Tree Space ($mathcal{JT}$), introduced by R. James, is the first Banach space constructed having non-separable conjugate and not containing $ell^1$. James actually proved that every infinite dimensional subspace of $mathcal{JT}$ contains a Hilbert space, which implies the $ell^1$ non-embedding. In this expository article, we present a direct proof of the $ell^1$ non-embedding, using Rosenthals $ell^1$- Theorem and some measure theoretic arguments, namely Rieszs Representation Theorem.
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