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:
“All of the great leaders have had one characteristic in common: it was the willingness to confront unequivocally the major anxiety of their people in their time. This, and not much else, is the essence of leadership.”
—John Kenneth Galbraith (b. 1908)
“Intellectual despair results in neither weakness nor dreams, but in violence.... It is only a matter of knowing how to give vent to one’s rage; whether one only wants to wander like madmen around prisons, or whether one wants to overturn them.”
—Georges Bataille (1897–1962)