Functional Analysis - Major and Foundational Results

Major and Foundational Results

Important results of functional analysis include:

  • The uniform boundedness principle (also known as Banach–Steinhaus theorem) applies to sets of operators with uniform bounds.
  • One of the spectral theorems (there is indeed more than one) gives an integral formula for the normal operators on a Hilbert space. This theorem is of central importance for the mathematical formulation of quantum mechanics.
  • The Hahn–Banach theorem extends functionals from a subspace to the full space, in a norm-preserving fashion. An implication is the non-triviality of dual spaces.
  • The open mapping theorem and closed graph theorem.

See also: List of functional analysis topics.

Read more about this topic:  Functional Analysis

Famous quotes containing the words major and/or results:

    The more you stay in this kind of job, the more you realize that a public figure, a major public figure, is a lonely man.
    Richard M. Nixon (1913–1995)

    Pain itself can be pleasurable accidentally in so far as it is accompanied by wonder, as in stage-plays; or in so far as it recalls a beloved object to one’s memory, and makes one feel one’s love for the thing, whose absence gives us pain. Consequently, since love is pleasant, both pain and whatever else results from love, in so far as they remind us of our love, are pleasant.
    Thomas Aquinas (c. 1225–1274)