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:
“A major misunderstanding of child rearing has been the idea that meeting a child’s needs is an end in itself, for the purpose of the child’s mental health. Mothers have not understood that this is but one step in social development, the goal of which is to help a child begin to consider others. As a result, they often have not considered their children but have instead allowed their children’s reality to take precedence, out of a fear of damaging them emotionally.”
—Elaine Heffner (20th century)
“The restlessness that comes upon girls upon summer evenings results in lasting trouble unless it is speedily controlled. The right kind of man does not look for a wife on the streets, and the right kind of girl waits till the man comes to her home for her.”
—Sedalia Times (1900)