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Working paper

Topological amenability and Köthe co-echelon algebras

arxiv.org. math. Cornell University, 2020. No. 2012.08956.
Pirkovskii A. Y., Piszczek K.
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.