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:
“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)
“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)