Timeline for Non-isometric Banach spaces
Current License: CC BY-SA 3.0
2 events
| when toggle format | what | by | license | comment | |
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| Jul 28, 2011 at 18:26 | comment | added | Robert Israel | Except that is not the case. Suppose $u$ and $v$ are a basis of your 2-dimensional subspace, and scalars are real. If $a u + b v$ and $c u + d v$ are in the unit sphere, the line segment joining them is in the unit sphere iff there is no index $j$ for which $(a u + b v)_j$ and $(c u + d v)_j$ have opposite sign. Take some $w \in l_1$ with all $w_j > 0$, let the sequence $\{\theta_j\}$ be dense in $[0, 2 \pi]$, and take $u_j = w_j \cos \theta_j$ and $v_j = w_j \sin \theta_j$. | |
| Jul 28, 2011 at 14:29 | history | answered | Gerald Edgar | CC BY-SA 3.0 |