# Amalgamated Spaces

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## Abstract

Let \(\rlap{--} x\, = \,(X,\Lambda,T,(x_t )_{t \in T} )\) be a Schauder tree basis and consider the corresponding ℓ_{2} Baire sum \(T_2 ^{\rlap{--} x}\) associated to \(\rlap{--} x\). The space \(T_2 ^{\rlap{--} x}\) contains, naturally, a complemented copy of every space in the class coded by the Schauder tree basis. Moreover, by Theorem 3.23, there is information on the kind of subspaces present in \(T_2 ^{\rlap{--} x}\). This is enough for a large number of applications. However, by Theorem 3.22, for every interesting Schauder tree basis \(\rlap{--} x\) the space \(T_2 ^{\rlap{--} x}\) contains an isomorphic copy of *c*_{0}.

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© Springer-Verlag Berlin Heidelberg 2010