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, points and/or view:
“He is the best sailor who can steer within the fewest points of the wind, and extract a motive power out of the greatest obstacles. Most begin to veer and tack as soon as the wind changes from aft, and as within the tropics it does not blow from all points of the compass, there are some harbors which they can never reach.”
—Henry David Thoreau (1817–1862)
“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)
“The view that honesty is something, and even a virtue, belongs, it is true, to those private opinions which are forbidden in this age of public opinions.”
—Friedrich Nietzsche (1844–1900)