The Kalton-Peck space as a spreading model - Suárez, Jesús (MATHEMATICA SCANDINAVICA, 2024)
The so-called Kalton-Peck space Z_2 is a twisted Hilbert space induced, using complex interpolation, by c_0 or _p for any 1≤ p eq 2<∞ . Kalton and Peck developed a scheme of results for Z_2 showing that it is a very rigid space. For example, every normalized basic sequence in Z_2 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 Z_2 to twisted Hilbert spaces Z(X) induced by asymptotic c_0 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 eq 2.