The Kalton-Peck space as a spreading model

The so-called Kalton-Peck space Z₂ is a twisted Hilbert space induced, using complex interpolation, by c₀ or ₚ for any 1≤ p≠ 2<∞. Kalton and Peck developed a scheme of results for Z₂ showing that it is a very rigid space. For example, every normalized basic sequence in Z₂ contains a subsequence which is equivalent to either the Hilbert copy ₂ or the Orlicz space M. Recently, new examples of twisted Hilbert spaces, which are induced by asymptotic ₚ-spaces, have appeared on the stage. Thus, our aim is to extend the Kalton-Peck theory of Z₂ to twisted Hilbert spaces $Z(X)$ induced by asymptotic c₀ or ₚ-spaces X for 1≤ p<∞. One of the novelties is to use spreading models to gain information on the isomorphic structure of the subspaces of a twisted Hilbert space. As a sample of our results, the only spreading models of $Z(X)$ are ₂ and M, whenever X is as above and p≠ 2.