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.