# rotund space

A normed space is said to be rotund if every point of $C(0,1)$ is an extreme point. Here $C(0,1)$ is the set $\{b:\lVert b\rVert=1\}$. Equivalently, a space is rotund if and only if $a\neq b$ and $\lVert a\rVert=\lVert b\rVert\leq 1$ implies $\lVert a+b\rVert<2$.

A uniformly convex space is rotund.

Title rotund space RotundSpace 2013-03-22 16:04:56 2013-03-22 16:04:56 Mathprof (13753) Mathprof (13753) 8 Mathprof (13753) Definition msc 46H05