On a class of Banach sequence spaces analogous to the space of Popov (Q2906106)

The author studies further properties of the Banach spaces \(Z_p\) for \(p \in {0} \cup [1,\infty)\) introduced by \textit{P. Azimi} and \textit{A. A. Ledari} [Czech. Math. J. 59, No. 3, 573--582 (2009; Zbl 1224.46017)]. The main initial property of these spaces is that \(Z_1\) is hereditarily \(\ell_1\) and does not have the Schur property. The main result asserts that no \(Z_p\) has the Schur property for any \(p \in {0} \cup [1,\infty)\) (which easily follows for \(p > 1\) from the fact that \(Z_p\) contains an isomorph of \(\ell_p\), and for \(p = 0\) that \(Z_0\) contains an isomorph of \(c_0\)). Another result of the paper shows that \(Z_1\) contains asymptotically isometric copies of \(\ell_1\).