Editing Functional analysis (section)

==Points of view==
Functional analysis includes the following tendencies:
*''Abstract analysis''. An approach to analysis based on [[topological group]]s, [[topological ring]]s, and [[topological vector space]]s.
*''Geometry of [[Banach space]]s'' 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, for example, [[Israel Gelfand]], to include most types of [[representation theory]].