Topological amenability and Köthe co-echelon algebras
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2020
- DOI:
- 10.48550/arXiv.2012.08956
- arXiv:
- arXiv:2012.08956
- Bibcode:
- 2020arXiv201208956P
- Keywords:
-
- Mathematics - Functional Analysis;
- 46H05;
- 46M18 (Primary) 46A04;
- 46A13;
- 46M05;
- 47B47 (Secondary)
- E-Print:
- 20 pages