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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
##### Keywords:
Banach lattice; lattice copy of $$\ell_\infty$$
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