# Hahn-Banach separation theorem for Hilbert spaces

What is the strongest form of the Hahn-Banach separation theorem for Hilbert spaces? Could you please provide a reference?

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Hi Tom! Do you have suggestions of what kinds of things a HB separation theorem on Hilbert space would accomplish that can't be done in Banach space? –  A Blumenthal Feb 13 at 16:54
Hi @ABlumenthal! Orthogonality of the separating hyperplanes to the distance-minimizing vector, relationship between the metric distance and the marginal difference between the hyperplanes, etc. –  Tom LaGatta Feb 13 at 17:23
Riesz representation. –  Michael Feb 13 at 18:05
Sorry, @Michael, that is not helpful. Could you expand on what you mean? The Riesz representation theorem is not a form of the Hahn-Banach separation theorem, though it is useful in stating it. –  Tom LaGatta Feb 13 at 19:31