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)
“For every life and every act
Consequence of good and evil can be shown
And as in time results of many deeds are blended
So good and evil in the end become confounded.”
—T.S. (Thomas Stearns)