Timeline for Do (Banach) ultrapowers carry some sort of 'elementary equivalence'?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 19, 2012 at 17:59 | vote | accept | Olaf Kummers | ||
| Apr 18, 2012 at 15:10 | answer | added | Bill Johnson | timeline score: 6 | |
| Apr 17, 2012 at 16:34 | comment | added | Bill Johnson | Sorry; I misread the question. | |
| Apr 17, 2012 at 6:41 | comment | added | Olaf Kummers | Please note $c_0$ has also this property. | |
| Apr 17, 2012 at 1:38 | comment | added | Yemon Choi | @Bill: I thought that the LT result referred to spaces for which every subspace is complemented, and not those for which only the subspaces isomorphic to the original are complemented? | |
| Apr 16, 2012 at 23:58 | comment | added | Bill Johnson | Juris gives good advice in his answer. As for your specific question, "suppose that we are given a Banach space X and each its subspace isomorphic to X is complemented. Is such property preserved under ultrapowers?", the answer is yes because Lindenstrauss and Tzafriri proved that such an X is isomorphic to a Hilbert space. | |
| Apr 16, 2012 at 23:51 | comment | added | Yemon Choi | In keeping with one of MO's guidelines, I really think it would be helpful if you could suggest some of these reasonable but non-trivial properties. "Is this true?" is an easier question to answer well than "What kinds of thing might be true?" | |
| Apr 16, 2012 at 23:05 | answer | added | Juris Steprans | timeline score: 6 | |
| Apr 16, 2012 at 22:44 | comment | added | Olaf Kummers | Yes, I am. Of course, I am asking about reasonable but non-trivial properties. | |
| Apr 16, 2012 at 22:40 | comment | added | Yemon Choi | The question "What properties are preserved by ultrapowers?" seems overly broad. I don't know the answer to the particular question you give at the end, though. Are you familiar with Heinrich's article Ultraproducts in Banach space theory, J. Reine Angew. Math. 313 (1980), 72--104? | |
| Apr 16, 2012 at 22:31 | history | asked | Olaf Kummers | CC BY-SA 3.0 |