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Dec 7, 2016 at 21:40 comment added Bill Johnson Well, $\beta = 2$ clearly does not imply reflexivity. Reform $\ell_2$ with the maximum of the $\ell_2$ norm and $\max_{j\not= k} |x(j)|+|x(k)|$ to make the unit vector basis elements a distance $2$ apart.
Dec 7, 2016 at 20:45 comment added anonymous As much as that's an interesting paper and I'm thankful for the reference: I don't think this answers any of my questions.
Dec 7, 2016 at 19:50 comment added Bill Johnson Tomek, look at $\sum \ell_1^n)_p$ as $p\to \infty$.
Dec 7, 2016 at 15:32 history answered Bill Johnson CC BY-SA 3.0