Strictly flat cyclic Fréchet modules and approximate identities
| dc.creator | Pirkovskii, A. Yu. | |
| dc.date | 2005-11-05 | |
| dc.date | 2006-05-05 | |
| dc.date.accessioned | 2026-07-07T06:50:50Z | |
| dc.date.available | 2026-07-07T06:50:50Z | |
| dc.description | Let A be a locally m-convex Fréchet algebra. We give a necessary and sufficient condition for a cyclic Fréchet A-module X=A_+/I to be strictly flat, generalizing thereby a criterion of Helemskii and Sheinberg. To this end, we introduce a notion of locally bounded approximate identity (a.i.), and we show that X is strictly flat if and only if the ideal I has a right locally bounded a.i. An example is given of a commutative locally m-convex Fréchet algebra that has a locally bounded a.i., but does not have a bounded a.i. On the other hand, we show that a quasinormable locally m-convex Fréchet algebra has a locally bounded a.i. if and only if it has a bounded a.i. Some applications to amenable Fréchet algebras are also given. | |
| dc.description | 8 pages; version 2: a mistake in Theorem 3 is corrected | |
| dc.identifier | https://arxiv.org/abs/math/0511132 | |
| dc.identifier | http://arxiv.org/abs/math/0511132 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104788 | |
| dc.subject | Functional Analysis | |
| dc.subject | Primary 46M18, 46M10, 46H25; Secondary 46A45, 16D40, 18G50 | |
| dc.title | Strictly flat cyclic Fréchet modules and approximate identities | |
| dc.type | text |