Timeline for Classification of subsymmetric basic sequences
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 16, 2016 at 19:32 | vote | accept | ragrigg | ||
| Mar 16, 2016 at 13:49 | comment | added | Ben W | Oh cool, that's a much simpler proof than I had in mind below. | |
| Mar 16, 2016 at 12:53 | comment | added | Bill Johnson | Yes, it is trivial that a subsymmetric basic sequence is bounded and bounded away from zero. If a basis is subsymmetric and not weakly null, then there is a bounded linear functional that is bounded away from zero on a subsequence of the basis, hence, by subsymmetry, there is another bounded linear functional that is bounded away from zero on the basis itself. Unconditionality then gives that the basis is equivalent to the unit vector basis of $\ell_1$. | |
| Mar 16, 2016 at 4:52 | comment | added | ragrigg | The definition that I am using for subsymmetric sequence requires the sequence to be unconditional. Under this definition, is a subsymmetric sequence always bounded away from zero? Do you know/have a reference/hint related to the dichotomy for subsymmetric sequences I stumbled upon? | |
| Mar 16, 2016 at 4:41 | history | answered | Bill Johnson | CC BY-SA 3.0 |