classification of separable Hilbert spaces

Let H1 and H2 be infinite dimensional, separable Hilbert spaces. Then there is an isomorphismPlanetmathPlanetmathPlanetmath f:H1H2 which is also an isometry.

In other words, H1 and H2 are identical as Hilbert spacesMathworldPlanetmath.

Title classification of separable Hilbert spaces
Canonical name ClassificationOfSeparableHilbertSpaces
Date of creation 2013-03-22 12:19:12
Last modified on 2013-03-22 12:19:12
Owner Evandar (27)
Last modified by Evandar (27)
Numerical id 5
Author Evandar (27)
Entry type Theorem
Classification msc 46C15
Related topic ClassificationOfHilbertSpaces