论文标题
常规多线性操作员的Arens扩展的订购连续性
Order continuity of Arens extensions of regular multilinear operators
论文作者
论文摘要
首先，我们给出了一个反例，表明无法改进多线性操作员Arens扩展的单独订单连续性结果，以在整个双方的乘积上获得单独的订单连续性。然后，我们在操作员和/或基础的Riesz空间/Banach Lattices上建立条件，以使扩展名在整个双方的乘积上是连续的。我们还证明，任何常规多线性操作员的所有Arens扩展都至少在一个变量中连续订购，并且我们研究Banach晶格$ e $上的常规均质多项式的Arens扩展是在$ e^{\ sim \ sim} $上连续订购的。
First we give a counterexample showing that recent results on separate order continuity of Arens extensions of multilinear operators cannot be improved to get separate order continuity on the product of the whole of the biduals. Then we establish conditions on the operators and/or on the underlying Riesz spaces/Banach lattices so that the extensions are order continuous on the product of the whole biduals. We also prove that all Arens extensions of any regular multilinear operator are order continuous in at least one variable and we study when Arens extensions of regular homogeneous polynomials on a Banach lattice $E$ are order continuous on $E^{\sim\sim}$.
