论文标题
Banach Lattices中的合并和注入性
Amalgamation and injectivity in Banach lattices
论文作者
论文摘要
我们研究Banach Lattices和晶格同构的类别$ \ Mathcal {Bl} $中的区分对象。 De Pagter和Wickstead引入的免费Banach格子结构可产生推出，并将其与凯勒勒在边际措施上的旧结果结合在一起，建立了Banach Lattices的合并性能。这将是证明$ l_1（[0,1]^{\ Mathfrak {c}}）$的关键工具，可以分开$ \ MATHCAL {BL} $注射剂，并提供了可分开的Sublattices通用式倾向的Banach Lattices的更多抽象示例。最后，对$ c（δ，l_1）$的理想分析，这是一个明显的通用班克晶格，如Leung，Li，Oikhberg和Tursi所示，这使我们能够得出结论，可以分开$ \ Mathcal {bl} $ - indentive banach lattices不可分离。
We study distinguished objects in the category $\mathcal{BL}$ of Banach lattices and lattice homomorphisms. The free Banach lattice construction introduced by de Pagter and Wickstead generates push-outs, and combining this with an old result of Kellerer on marginal measures, the amalgamation property of Banach lattices is established. This will be the key tool to prove that $L_1([0,1]^{\mathfrak{c}})$ is separably $\mathcal{BL}$-injective, as well as to give more abstract examples of Banach lattices of universal disposition for separable sublattices. Finally, an analysis of the ideals on $C(Δ,L_1)$, which is a separably universal Banach lattice as shown by Leung, Li, Oikhberg and Tursi, allows us to conclude that separably $\mathcal{BL}$-injective Banach lattices are necessarily non-separable.
