论文标题
拓扑修正性和Köthe共同代数
Topological amenability and Köthe co-echelon algebras
论文作者
论文摘要
我们介绍了拓扑平坦的本地凸模块的概念，该模块扩展了平坦的Banach模块的概念，并且非常适合不可过度的设置（尤其是DF模型的设置）。通过使用此概念，我们引入了拓扑上的本地凸代代数，我们表明，当且仅当它是约翰逊（Johnson）的情况下，就可以在拓扑上进行拓扑df-elgebra，从而扩展了Helemskii-Sheinberg，从而延伸了Banach Algebras的标准。作为一种应用，我们完全表征了拓扑上的Kötheco-echelon代数。
We introduce a notion of a topologically flat locally convex module, which extends the notion of a flat Banach module and which is well adapted to the nonmetrizable setting (and especially to the setting of DF-modules). By using this notion, we introduce topologically amenable locally convex algebras and we show that a complete barrelled DF-algebra is topologically amenable if and only if it is Johnson amenable, extending thereby Helemskii-Sheinberg's criterion for Banach algebras. As an application, we completely characterize topologically amenable Köthe co-echelon algebras.
