So here it was shown in an infinite dimensional seperable Hilbert space $H$, with the orthonormal basis $E=\{e_1,e_2,\dots \}$ that $0\in \overline{E}^w$, where the right hand side denotes the weak closure of $E$. Can someone explain how the Riesz Representation theorem is used here?
2026-03-26 11:17:38.1774523858
Riesz Representation Theorem & Weak closure of orthonormal basis in Hilbert space
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You don't need Riesz Representation here. As shown in Cameron's answer, all you need is Bessel's inequality.