If $H$ is a Hilbert space, $U≤H$ is closed and $E≤U^⊥$ such that $x∈H$ with $x⊥_H E$ implies $x∈U$, then $U^⊥=\overline E^{\langle\;⋅\;,\;⋅\;\rangle}$

score 1k · Answer 14 · 2026-04-15 09:18:28

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Inner product induced norm vs $l_2$ norm

Published on 15 Apr 2026 - 9:18

score 90 · Answer 15 · 2026-04-16 13:03:59

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Prove $\Bigg(\langle\nabla f(x),x \rangle = af(x) \Bigg) \Leftrightarrow \Bigg(f(tx)=t^af(x) \Bigg)$ for $f: \Bbb R^n \to \Bbb R$ differentiable

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If $H$ is a Hilbert space, $U≤H$ is closed and $E≤U^⊥$ such that $x∈H$ with $x⊥_H E$ implies $x∈U$, then $U^⊥=\overline E^{\langle\;⋅\;,\;⋅\;\rangle}$

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