Points of View
Functional analysis in its present form includes the following tendencies:
- Abstract analysis. An approach to analysis based on topological groups, topological rings, and topological vector spaces.
- Geometry of Banach spaces contains many topics. One is combinatorial approach connected with Jean Bourgain; another is a characterization of Banach spaces in which various forms of the law of large numbers hold.
- Noncommutative geometry. Developed by Alain Connes, partly building on earlier notions, such as George Mackey's approach to ergodic theory.
- Connection with quantum mechanics. Either narrowly defined as in mathematical physics, or broadly interpreted by, e.g. Israel Gelfand, to include most types of representation theory.
Read more about this topic: Functional Analysis
Famous quotes containing the words points of view, points of, points and/or view:
“The dominant metaphor of conceptual relativism, that of differing points of view, seems to betray an underlying paradox. Different points of view make sense, but only if there is a common co-ordinate system on which to plot them; yet the existence of a common system belies the claim of dramatic incomparability.”
—Donald Davidson (b. 1917)
“Type of the wise, who soar, but never roam—
True to the kindred points of Heaven and Home!”
—William Wordsworth (1770–1850)
“When our relatives are at home, we have to think of all their good points or it would be impossible to endure them. But when they are away, we console ourselves for their absence by dwelling on their vices.”
—George Bernard Shaw (1856–1950)
“Currently, U.S. society has been encouraged by its political and subsidized mass-media intelligentsia to view U.S. life as a continual “morning in America” paradise, where the only social problems occur in the inner cities. Psychologists call this denial.”
—Ishmael Reed (b. 1938)