Timeline for Does there exists an extreme point $(a_1^,...,a_n^)$ of $B_{\mu^}$ such that $a_i^\neq 0$ for all $1\leq i\leq n$ and $\sum_{I=1}^n a_i^*a_i=1?$

6 events

when toggle format	what		by	license	comment
Jul 23, 2018 at 14:58	vote	accept	Idonknow
Jul 23, 2018 at 14:35	history	edited	Mikhail Ostrovskii	CC BY-SA 4.0	added the last paragraph
Jul 23, 2018 at 13:40	comment	added	Mikhail Ostrovskii		Yes, in the current example $n\ge 4$. One can modify to get $n\ge 3$ by looking at $\ell_\infty^2\oplus_2 \ell_2^{n-2}$. The answer to the second question is "Yes".
Jul 23, 2018 at 8:24	comment	added	Idonknow		Just to clarify, in your example, you are letting $\mu^* = \\|\cdot\\|_\infty \oplus_\infty \\|\cdot\\|_2$ where the formal norm is on first two components while the latter norm is on remaining $n-2$ compoenents?
Jul 23, 2018 at 6:35	comment	added	Idonknow		I suppose that $n\geq 4?$
Jul 22, 2018 at 15:14	history	answered	Mikhail Ostrovskii	CC BY-SA 4.0

Timeline for Does there exists an extreme point $(a_1^*,...,a_n^*)$ of $B_{\mu^*}$ such that $a_i^*\neq 0$ for all $1\leq i\leq n$ and $\sum_{I=1}^n a_i^*a_i=1?$