Properties
- The Milman–Pettis theorem states that every uniformly convex Banach space is reflexive, while the converse is not true.
- If is a sequence in a uniformly convex Banach space which converges weakly to and satisfies, then converges strongly to, that is, .
- A Banach space is uniformly convex if and only if its dual is uniformly smooth.
- Every uniformly convex space is strictly convex.
Read more about this topic: Uniformly Convex Space
Famous quotes containing the word properties:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)