classification of separable Hilbert spaces

Let $H_1$ and $H_2$ be infinite dimensional, separable Hilbert spaces. Then there is an isomorphism $f:H_1\to H_2$ which is also an isometry.

In other words, $H_1$ and $H_2$ are identical as Hilbert spaces.

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