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)
“Sometimes apparent resemblances of character will bring two men together and for a certain time unite them. But their mistake gradually becomes evident, and they are astonished to find themselves not only far apart, but even repelled, in some sort, at all their points of contact.”
—Sébastien-Roch Nicolas De Chamfort (1741–1794)
“Wonderful “Force of Public Opinion!” We must act and walk in all points as it prescribes; follow the traffic it bids us, realise the sum of money, the degree of “influence” it expects of us, or we shall be lightly esteemed; certain mouthfuls of articulate wind will be blown at us, and this what mortal courage can front?”
—Thomas Carlyle (1795–1881)
“Beauty depends on size as well as symmetry. No very small animal can be beautiful, for looking at it takes so small a portion of time that the impression of it will be confused. Nor can any very large one, for a whole view of it cannot be had at once, and so there will be no unity and completeness.”
—Aristotle (384 B.C.–322 B.C.)