Existence of complemented subspaces isomorphic to \(l^{q}\) in quasi Banach interpolation spaces (Q1024975)

Let \((E_0,E_1)\) be a compatible couple of quasi Banach spaces and \(0<\theta<1\), \(0<q<\infty\). The author presents a sufficient condition that the quasi Banach interpolation space \((E_0,E_1)_{\theta,q}\) has complemented subspaces isomorphic to \(l^q\), complementing the author's previous results on containment of (not necessarily complemented) subspaces isomorphic to \(l^q\) in [\textit{J.\,A.\thinspace López Molina}, Turk.\ J.\ Math.\ 24, No.\,4, 373--378 (2000; Zbl 0983.46004)]. An application to couples of \(l^p\)-spaces is presented.