Contribution to the classification of minimal extensions
type: Item
instance of: scholarly article
title: Contribution to the classification of minimal extensions
zbMATH Open document ID: 1059.46008
author: Félix Cabello Sánchez
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-09-23T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 46B03
Mathematics Subject Classification ID: 46B45
Mathematics Subject Classification ID: 46A16
zbMATH DE Number: 2102583
zbMATH Keywords: minimal extension
zbMATH Keywords: Banach space
zbMATH Keywords: quasi-Banach space
MaRDI profile type: Publication
full work available at URL: j.na.2004.03.031
OpenAlex ID: W2001982902
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DOI: 10.1016/J.NA.2004.03.031
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description: scientific article; zbMATH DE number 2102583