We show that \(c_0\) is not a projective Banach lattice, answering a question of B. de Pagter and A. Wickstead. .On the other hand, we show that \(c_0\) is complemented in the free Banach lattice generated by itself (seen as a Banach space). As a consequence, the free Banach lattice generated by \(c_0\) is not projective.

中文翻译：

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在Banach格上$$ c_0 $$ c 0

我们证明\（c_0 \）不是射影的Banach格，回答了B. de Pagter和A. Wickstead的问题。另一方面，我们证明\（c_0 \）在自身生成的自由Banach晶格中被补充（称为Banach空间）。结果，由\（c_0 \）生成的自由Banach晶格不是投影的。