Kalton, N. J. Banach envelopes of non-locally convex spaces. (English) Zbl 0577.46016 Can. J. Math. 38, 65-86 (1986). Let X be a non-locally convex quasi-Banach space with separating dual. We give conditions which imply that \(X^*\) cannot have finite cotype. These conditions imply that most naturally arising spaces X cannot have \(c_ 0\) as a Banach envelope. However, we also construct a space with \(c_ 0\) as its Banach envelope. Finally we show that for any separable Banach space Z there is a subspace X of \(\ell_ p\) \((0<p<1)\) whose Banach envelope is isomorphic to \(\ell_ 1\oplus Z\). Cited in 12 Documents MSC: 46B25 Classical Banach spaces in the general theory 46B20 Geometry and structure of normed linear spaces Keywords:non-locally convex quasi-Banach space with separating dual; finite cotype; Banach envelope PDF BibTeX XML Cite \textit{N. J. Kalton}, Can. J. Math. 38, 65--86 (1986; Zbl 0577.46016) Full Text: DOI OpenURL