Uniqueness of the unconditional basis of \(\ell_{1}(\ell_p)\) and \(\ell_p(\ell_1)\), \(0<p<1\)
It was shown by \textit{C. Leránoz} [Stud. Math. 102, 193--207 (1992; Zbl 0812.46003)] that the spaces \(c_0(\ell_p)\) \((0<p<1)\) have a unique normalized unconditional basis up to permutation and, later on, the authors proved in [Stud. Math. 150, 35--52 (2002; Zbl 1031.46006)] the uniqueness of an unconditional basis up to permutation of \(\ell_p(c_0)\) and \(\ell_p(\ell_2)\) for \(0<p<1\). Here the same result is proved for the quasi-Banach spaces \(\ell_1(\ell_p)\) and \(\ell_p(\ell_1)\) \((0<p<1)\): they have a unique unconditional basis up to a permutation.
scientific article; zbMATH DE number 2175439