Timeline for What (classes of) Banach spaces are known to have Schauder basis?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 6, 2013 at 4:04 | vote | accept | Clark Chong | ||
| Jul 5, 2013 at 21:56 | comment | added | Clark Chong | Casazza seems to have mentioned a "counterexample" in his handbook article - there exists a reflexive subspace of $l_p$ that fails Compact Approximation Property --> this would be a UC space which fails property $\pi$ | |
| Jul 5, 2013 at 21:54 | comment | added | Clark Chong | 1) Do you know if anyone has considered the relation between Uniform Convex space and $\pi$ spaces? (J Diestel's "Geometry of Banach Spaces - Selected Topics" contains some info about the case when a UC space HAS a basis, while I am trying to see if there are classes of UC spaces known to have a basis) 2) In particular, do you know if $C_p$, the Banach space of Schatten-p class operators on a Hilbert space has property $\pi$? Thank you so much! | |
| Jul 5, 2013 at 21:50 | comment | added | Clark Chong | Thanks for the references given. I have read them except for Singer's two volumes and learnt a lot. I have the impression: the articles available are all trying to show the relation between the different properties -- in particular, whether they are distinct from each other and when a weaker property implies existence of basis. I couldn't find one which illustrate how to show a space has property $\pi$. So, here are my two questions: | |
| Jun 27, 2013 at 2:04 | history | answered | Bill Johnson | CC BY-SA 3.0 |