Examples
- Every Hilbert space is uniformly convex.
- Every closed subspace of a uniformly convex Banach space is uniformly convex.
- Hanner's inequalities imply that Lp spaces are uniformly convex.
- Conversely, is not uniformly convex. For example, in consider and . Then and, but .
Read more about this topic: Uniformly Convex Space
Famous quotes containing the word examples:
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)