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
Canonical name	RotundSpace
Date of creation	2013-03-22 16:04:56
Last modified on	2013-03-22 16:04:56
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	8
Author	Mathprof (13753)
Entry type	Definition
Classification	msc 46H05