A remark on bases in quotients of ell<sub>p</sub> when 0 < p < 1


In [9] Stiles showed that if 0 < p < 1, \ell<sub>p</sub> has an infinite-dimensional closed subspace which contains no complemented copy of \ell<sub>p</sub>; this contrasts with the well-known result of Pelczynski [5] for 1≤ p < ∈fty. The following curious theorem is the main result of this note: Theorem 1. Let M be an infinite-dimensional closed subspace of \ell<sub>p</sub> where 0 < p < 1. Suppose \ell<sub>p</sub>/M has a basis. Then M contains a subspace isomorphic to \ell<sub>p</sub> and complemented in \ell<sub>p</sub>.

DOI Code: 10.1285/i15900932v11p231

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