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
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