Functional Analysis - Points of View

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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