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I am seeking a reference that says:

If $V \subset H \subset V^*$ is a Gelfand triple with all spaces Hilbert spaces and if $V \subset H$ is a compact embedding, then there is a basis of $V$ which is orthogonal wrt. $V$ and orthonormal wrt. $H$.

I know how to prove but I just want something to cite. Anyone have any ideas? I tried the usual sources but had no luck.

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  • $\begingroup$ Can't you just write something like "the Hilbert-Schmidt representation of the compact embedding gives a common orthonogal basis"? References to the Hilbert-Schmidt representation theorem are easily available. $\endgroup$
    – Jochen Wengenroth
    Commented Oct 1, 2014 at 13:21
  • $\begingroup$ OK, I just wanted to provide link for some readers but maybe I can just write it. $\endgroup$
    – MMML
    Commented Oct 1, 2014 at 16:47

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