# classification of separable Hilbert spaces

Let $H_{1}$ and $H_{2}$ be infinite dimensional, separable Hilbert spaces. Then there is an isomorphism $f:H_{1}\rightarrow H_{2}$ which is also an isometry.

In other words, $H_{1}$ and $H_{2}$ are identical as Hilbert spaces.

Title classification of separable Hilbert spaces ClassificationOfSeparableHilbertSpaces 2013-03-22 12:19:12 2013-03-22 12:19:12 Evandar (27) Evandar (27) 5 Evandar (27) Theorem msc 46C15 ClassificationOfHilbertSpaces