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)
“The two great points of difference between a democracy and a republic are: first, the delegation of the government, in the latter, to a small number of citizens elected by the rest; secondly, the greater number of citizens and greater sphere of country over which the latter may be extended.”
—James Madison (1751–1836)
“The men who carry their points do not need to inquire of their constituents what they should say, but are themselves the country which they represent: nowhere are its emotions or opinions so instant and so true as in them; nowhere so pure from a selfish infusion.”
—Ralph Waldo Emerson (1803–1882)
“In view of this half-sight of science, we accept the sentence of Plato, that, “poetry comes nearer to vital truth than history.””
—Ralph Waldo Emerson (1803–1882)