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The lattice-isometric copies of \(\ell_{\infty}(\Gamma)\) in quotients of Banach lattices. (English) Zbl 1033.46009
Summary: Let \(E\) be a Banach lattice and let \(M\) be a norm-closed and Dedekind \(\sigma\)-complete ideal of \(E\). If \(E\) contains a lattice-isometric copy of \(\ell_{\infty}\), then \(E/M\) contains such a copy as well, or \(M\) contains a lattice copy of \(\ell_{\infty}\). This is one of the consequences of more general results presented in this paper.

MSC:
46B04 Isometric theory of Banach spaces
46B25 Classical Banach spaces in the general theory
46B42 Banach lattices
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