Contribution to the classification of minimal extensions (Q1879763)

Some minimal extensions of \(\ell_1\) are studied. It is shown that some certain quasi-Banach spaces arising from quasi-linear functions on~\(\ell_1\) are not isomorphic: in particular, it is proved that \textit{M. Ribe's} space [Proc. Am. Math. Soc. 73, 351--355 (1979; Zbl 0397.46002)] contains no isomorphic copy of that of \textit{N. J. Kalton} [Compos. Math. 37, 243--276 (1978; Zbl 0395.46003)]. Also, a continuum of mutually non-isomorphic (Ribe like) minimal extensions of~\(\ell_1\) is constructed.