Timeline for A question on probability measure on the unit ball of Banach spaces
Current License: CC BY-SA 3.0
7 events
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| Jul 7, 2017 at 1:40 | comment | added | Dongyang Chen | @ChristianRemling Why is it impossible that $|<x^{*},x>|=1$ a.e. for every fixed $\|x\|=1$? | |
| Jul 6, 2017 at 16:39 | comment | added | Christian Remling | Let $\mu$ be a prob measure, and take any $\|x\|=1$. The LHS equals $1$. On the RHS $|\langle x^*, x\rangle |\le \|x^*\|\le 1$, so to make the integral $\ge 1$, we'd have to have $|\langle x^*, x\rangle|=1$ a.e. for every fixed $x$, which is clearly impossible. | |
| Jul 6, 2017 at 14:18 | comment | added | Dongyang Chen | @ChristianRemling Could you give a detailed proof of your above statement? I do not understand your statement well. | |
| Jul 5, 2017 at 18:05 | comment | added | Christian Remling | This is hopeless. Take $X=\ell^1$ (maybe two-dimensional, for simplicity), $e_1, e_2\in X^*$ as your sequence for a counterexample. | |
| Jul 5, 2017 at 17:56 | history | edited | Christian Remling | CC BY-SA 3.0 |
added 49 characters in body
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| Jul 5, 2017 at 12:44 | history | edited | Henry.L |
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| Jul 5, 2017 at 12:41 | history | asked | Dongyang Chen | CC BY-SA 3.0 |