Recently, Wickstead investigated the long-standing problem of adding an identity to a non-unital Banach lattice algebra. In this regard, he proved that, in the category whose objects are unital Banach lattice algebras and morphisms are identity preserving algebra and lattice homomorphisms, there is no reflection for \(c_{0}\) in which \(c_{0}\) can be embedded as an algebra and order ideal. The main purpose of this note is to describe an alternative category in which a suitable reflection of \(c_{0}\) can be located, producing a satisfactory lattice unitization of \(c_{0}\) with \(c_{0}\) as an algebra and order ideal.

最近，威克斯特德（Wickstead）研究了向非单位Banach格代数添加身份的长期存在的问题。就这一点而言，他证明了，在对象为单位Banach格代数且态射是恒等式保全代数和晶格同态的类别中，对于\（c_ {0} \）其中\（c_ {0} \ ）可以作为代数和有序理想嵌入。本注释的主要目的是描述一个替代类别，在其中可以定位\（c_ {0} \）的适当反射，从而产生令人满意的\（c_ {0} \）与\（c_ {0 } \）作为代数和阶理想。