Timeline for Amenable Banach algebras -- homological characterization
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 18, 2017 at 12:03 | comment | added | Krzysztof | I know this paper by Pirkovskii - it is mainly devoted to Fr\'echet algebras. The crucial fact (from the view point of my category) he is using is the duality between exact sequences, i.e. a short sequence of Fr\'echet spaces is exact iff its dual sequence is exact. Although DF-spaces are dual to Fr\'echet ones, the above fact is not true in this category. Of course I can take the bidual sequence to the initial one but a DF-space is not in general a subspace in its second dual. | |
| Jul 13, 2017 at 18:07 | comment | added | Yemon Choi | Does projecteuclid.org/euclid.hha/1251832561 help at all? | |
| Jul 13, 2017 at 8:33 | comment | added | Krzysztof | If I guess correctly, you're thinking about the relation $X$ - flat $\Leftrightarrow$ $X^*$ - injective. In the category I am working in (DF-spaces) duals of DF are not DF. Therefore I turned my attention to Lemma 0.5.1. But this Lemma needs the OMT. Therefore my ``last chance'' is a direct proof. That's at least all I can figure out. | |
| Jul 12, 2017 at 3:41 | comment | added | Yemon Choi | What category are you using? If I recall correctly, going from "$H^1(A,X^*)=0$" to "$H_0(A,X)$ is Hausdorff" uses duality theory of Banach spaces, but not the open mapping theorem. However, it has been a long time since I worked through the details from first principles | |
| Jun 29, 2017 at 11:37 | history | asked | Krzysztof | CC BY-SA 3.0 |