Timeline for Martingale-cotype vs cotype on super-reflexive spaces
Current License: CC BY-SA 3.0
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| May 6, 2013 at 10:02 | comment | added | user33709 | My feeling is that the answer is false and that you need to study the exemples of super-reflexive spaces which are not UMD. Maybe, one of them is a counter-example to your question. See the recent paper front.math.ucdavis.edu/1112.0739 for information on all known counter-examples. | |
| May 5, 2013 at 20:48 | comment | added | Jason Rute | Cédric, I found the article, link.springer.com/article/10.1007%2FBF02384306, but I am not sure I understand your comment. Are you saying if I understood this example, I might be able to answer my question? | |
| May 5, 2013 at 11:03 | comment | added | user33709 | Undoubtedly, you must look at the Bourgain's exemple of supereflexive space failing UMD and see... | |
| May 5, 2013 at 10:50 | comment | added | Jason Rute | Thanks. I assume you mean to say "$X$ is isomorphic to a $q$-uniformly convex space". (It seems that $\mathsf{UMD}$ is preserved under isomorphisms, where as uniform convexity is not. That is of course if we are using the same definition of $q$-uniformly convex.) Also, I'm still hoping for an answer to my main question, but maybe $\mathsf{UMD}$ is the best known. | |
| May 5, 2013 at 10:31 | history | edited | user33709 | CC BY-SA 3.0 |
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| May 5, 2013 at 9:53 | history | answered | user33709 | CC BY-SA 3.0 |