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 three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.”
—Willard Van Orman Quine (b. 1908)
“There are good points about all such wars. People forget self. The virtues of magnanimity, courage, patriotism, etc., etc., are called into life. People are more generous, more sympathetic, better, than when engaged in the more selfish pursuits of peace.”
—Rutherford Birchard Hayes (1822–1893)
“Thy fair virtue’s force perforce doth move me
On the first view to say, to swear, I love thee.”
—William Shakespeare (1564–1616)