On subspaces isomorphic to l^q in interpolation of quasi Banach spaces

Authors: J. A. LOPEZ MOLINA

Abstract: We show that every sequence $\{x_n\}_{n=1}^{\infty}$ in a real interpolation space $(E_0,E_1)_{\theta,q}$, $0 < \theta < 1$, $0 < q < \infty,$ of quasi Banach spaces $E_0,E_1,$ which is $0-$convergent in $E_0 + E_1$ but $\inf_n \;\|x_n\|_{(E_0,E_1)_{\theta,q}} > 0,$ has a subsequence which is equivalent to the standard unit basis of $\ell^q.$

Keywords: real interpolation method, quasi Banach spaces.

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