论文标题
Godefroy-Kalton的免费Banach Lattices原则
A Godefroy-Kalton principle for free Banach lattices
论文作者
论文摘要
由Godefroy和Kalton引入的Banach空间的Lipschitz延伸特性的动机，我们考虑了散布晶格的特性，这是Banach晶格和晶格同质性类别中的类似概念。也就是说，如果每个晶格同构为$ x $具有有界线性的右内方右侧的晶格同构，则必须具有晶格同质性右倒入，则可以满足晶格的属性。在免费的Banach晶格方面，可以将其改编为以下问题：哪个Banach Lattices嵌入了免费的Banach晶格中，它们作为晶格填充的Sublattice产生？我们将为Banach晶格提供必要的条件，使其拥有晶格的属性，并表明该物业是由Banach Spaces共享的，其$ 1 $ - 条件和免费的Banach Lattices。 $ c（k）$空间的情况也将进行分析。
Motivated by the Lipschitz-lifting property of Banach spaces introduced by Godefroy and Kalton, we consider the lattice-lifting property, which is an analogous notion within the category of Banach lattices and lattice homomorphisms. Namely, a Banach lattice $X$ satisfies the lattice-lifting property if every lattice homomorphism to $X$ having a bounded linear right-inverse must have a lattice homomorphism right-inverse. In terms of free Banach lattices, this can be rephrased into the following question: which Banach lattices embed into the free Banach lattice which they generate as a lattice-complemented sublattice? We will provide necessary conditions for a Banach lattice to have the lattice-lifting property, and show that this property is shared by Banach spaces with a $1$-unconditional basis as well as free Banach lattices. The case of $C(K)$ spaces will also be analyzed.
