Definition:Hilbert Space/Definition 2
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Definition
Let $H$ be a vector space over $\mathbb F \in \set {\R, \C}$.
Let $\struct {H, \norm {\,\cdot\,}_H}$ be a Banach space with norm $\norm {\,\cdot\,}_H : H \to \R_{\ge 0}$.
Let $H$ have an inner product $\innerprod \cdot \cdot_H : H \times H \to \C$ such that the inner product norm is equivalent to the norm $\norm {\,\cdot\,}_H$.
Then $H$ is a Hilbert space over $\mathbb F$.
Also see
- Results about Hilbert spaces can be found here.
Source of Name
This entry was named for David Hilbert.