发表机构
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过引入与算子相关的新工具，研究了自由 p-凸巴拿赫格及相关格的上界性质，揭示了 Fatou 性质与 Radon-Nikodym 性质的联系，并给出非正则子格的例子。
AI 中文摘要
已知巴拿赫空间 $X$ 上的自由 $p$-凸巴拿赫格可以表示为 $X^*$ 单位球上的函数空间。由此，它产生了某些相关的（更大的）格。为了研究这样的格，我们引入了一个新工具，该工具与到 $X$ 的算子有关。该工具被用于（i）确定所考虑的格是否具有或缺乏涉及向上有向集的上界的性质，即 Fatou 性质和相关的单调有界性质；（ii）研究所考虑空间之间嵌入的正则性。我们发现了 ${\textrm{FBL}}^{(p)}[X]$ 的类 Fatou 性质与 $X$ 的 Radon-Nikodym 性质之间的联系。此外，我们给出了一个 $X \subset Y$ 的例子，使得 ${\textrm{FBL}}^{(p)}[X]$ 不是 ${\textrm{FBL}}^{(p)}[Y]$ 的正则子格。
英文摘要
It is known that the free $p$-convex Banach lattice on a Banach space $X$ can be represented as a space of functions on the unit ball of $X^*$. In this way, it gives rise to certain related (larger) lattices. To investigate such lattices, we introduce a new tool, related to operators into $X$. This tool is then used to (i) determine whether the lattices in question possess, or fail, properties involving upper bounds of upward directed sets -- namely, the Fatou property, and the related property of monotonic boundedness; (ii) investigate the regularity of embeddings between spaces in question. We find connections between the Fatou-like properties of ${\textrm{FBL}}^{(p)}[X]$ and the Radon-Nikodym property of $X$. In addition, we give an example of $X \subset Y$ such that ${\textrm{FBL}}^{(p)}[X]$ is not a regular sublattice of ${\textrm{FBL}}^{(p)}[Y]$.
Comments28 pages
