Abstract: We study the six diagrams generated by the first three Schechter interpolators ?2(f)=f´´(1/2)/2!,?1(f)=f´(1/2),?0(f)=f(1/2) acting on the Calderón space associated to the pair (l?,l1). We will study the remarkable and somehow unexpected properties of all the spaces appearing in those diagrams: two new spaces (and their duals), two Orlicz spaces (and their duals) in addition to the third order Rochberg space, the standard Kalton-Peck space Z2 and, of course, the Hilbert space Z2. We will also deal with a nice test case: that of weighted l2 spaces, in which case all involved spaces are Hilbert spaces.

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