Hilbert space
A Hilbert space
is an inner product space
which is http://planetmath.org/node/603complete
under the metric.
In particular, a Hilbert space is a Banach space in the norm by the inner product
, since the norm and the inner product both induce the same metric. Any finite-dimensional inner product space is a Hilbert space, but it is worth mentioning that some authors require the space to be infinite dimensional for it to be called a Hilbert space.
| Title | Hilbert space |
| Canonical name | HilbertSpace |
| Date of creation | 2013-03-22 12:19:06 |
| Last modified on | 2013-03-22 12:19:06 |
| Owner | mathcam (2727) |
| Last modified by | mathcam (2727) |
| Numerical id | 11 |
| Author | mathcam (2727) |
| Entry type | Definition |
| Classification | msc 46C05 |
| Related topic | InnerProductSpace |
| Related topic | HilbertModule |
| Related topic | QuadraticFunctionAssociatedWithALinearFunctional |
| Related topic | VectorNorm |
| Related topic | RieszSequence |
| Related topic | VonNeumannAlgebra |
| Related topic | HilbertSpacesAndQuantumGroupsVonNeumannAlgebras |
| Related topic | L2SpacesAreHilbertSpaces |
| Related topic | QuantumGroupsAndVonNeumannAlgebras |
| Related topic | HAlgebra |
| Related topic | Ries |