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
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“Type of the wise, who soar, but never roam—
True to the kindred points of Heaven and Home!”
—William Wordsworth (1770–1850)
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An’ each for other’s weelfare kindly spiers:
The social hours, swift-winged, unnoticed fleet;
Each tells the uncos that he sees or hears;
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Anticipation forward points the view:”
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