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A Hilbert space $H$ is a real or complex vector space endowed with an inner product such that $H$ is a complete metric space when endowed with the norm induced by this inner product.

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volume of parallelotope in $L^2(\mathbb R).$ [closed]

Let $L^2(\mathbb R)$ is complex Hilbert space with standard inner product. Does it make sense to talk of volume of parallelotope formed by following vectors in $L^2(\mathbb R):$ say, e.g., $$\{ …
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