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:
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—Sébastien-Roch Nicolas De Chamfort (1741–1794)
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—Stefan Zweig (18811942)
“That author who draws a character, even though to common view incongruous in its parts, as the flying-squirrel, and, at different periods, as much at variance with itself as the caterpillar is with the butterfly into which it changes, may yet, in so doing, be not false but faithful to facts.”
—Herman Melville (1819–1891)