Timeline for Block version of Maurey Pisier theorem
Current License: CC BY-SA 3.0
9 events
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| Nov 15, 2016 at 18:25 | comment | added | user | I didn't compute exactly the best block type of the summing basis, but by comparing it to the Rademacher functions, you can deduce it must be somewhere in [1,2], and none of these $\ell_p$ spaces is block finitely representable in the summing basis. This does give a counterexample without knowing the exact block type. | |
| Nov 15, 2016 at 11:51 | vote | accept | user | ||
| Nov 14, 2016 at 23:45 | comment | added | Bunyamin Sari | You may also want to check if Example 6.4 of the paper by Knaust, Odell and Schlumprecht is relevant. | |
| Nov 14, 2016 at 23:29 | history | edited | Bunyamin Sari | CC BY-SA 3.0 |
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| Nov 14, 2016 at 23:09 | history | edited | Bunyamin Sari | CC BY-SA 3.0 |
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| Nov 14, 2016 at 23:04 | comment | added | Bunyamin Sari | I agree that one has to compute the block type of summing basis. So i revised my answer. I even believed there are unconditional counterexamples but i do not know any now. | |
| Nov 14, 2016 at 23:02 | history | edited | Bunyamin Sari | CC BY-SA 3.0 |
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| Nov 14, 2016 at 22:19 | comment | added | user | It is clear that the summing basis does not have any block type better than 2, but is it clear that it does not have any block type better than 1? Otherwise the non-block finite representability of $\ell_1^n$ in the summing basis isn't a counterexample. Is there an easy counterexample for the same question for block cotype? | |
| Nov 14, 2016 at 21:22 | history | answered | Bunyamin Sari | CC BY-SA 3.0 |