论文标题
评估在截短的函数截短栅栏上的同态特征
Evaluating characterizations of homomorphisms on truncated vector lattices of functions
论文作者
论文摘要
令$ l $为（非一定是UNICAL）的截断矢量晶格，是非空置套装$ x $上的实用值。 $ l $上的非零线性功能$ψ$如果保留截断，则称为截断同构，即，即％\ [ψ\ left（f \ wedge \ wedge \ mathbf {1} _ {x} _ {x} \ right） } f \ in L. \ \]我们证明，$ l $上的线性功能$ψ$是且仅当$ψ$是晶格同构时的截断同质性同态，并且％\ [\ sup \ sup \ sup \ left \ left \ {ψ\ {ψ\ left（f \ right） \]这使我们能够证明截断同态的不同评估表征。在这方面，特别注意连续案例，现有文献的各种结果被普遍化。
Let $L$ be a (non necessarily unital) truncated vector lattice of real-valued functions on a nonempty set $X$. A nonzero linear functional $ψ$ on $L$ is called a truncation homomorphism if it preserves truncation, i.e.,% \[ ψ\left( f\wedge\mathbf{1}_{X}\right) =\min\left\{ ψ\left( f\right) ,1\right\} \text{ for all }f\in L. \] We prove that a linear functional $ψ$ on $L$ is a truncation homomorphism if and only if $ψ$ is a lattice homomorphism and% \[ \sup\left\{ ψ\left( f\right) :f\leq\mathbf{1}_{X}\right\} =1. \] This allows us to prove different evaluating characterizations of truncation homomorphisms. In this regard, a special attention is paid to the continuous case and various results from the existing literature are generalized.
