Hilbert space

A Hilbert spaceMathworldPlanetmath is an inner product spaceMathworldPlanetmath which is http://planetmath.org/node/603completePlanetmathPlanetmath under the metric.

In particular, a Hilbert space is a Banach spaceMathworldPlanetmath in the norm by the inner productMathworldPlanetmath, 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
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