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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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Commutator of self-adjoint operators and $C^1$-type formula

Let $\mathcal{H}$ be a (complex) Hilbert space. Let $H$ be a self-adjoint operator on $\mathcal{H}$ with dense domain $\mathcal{D}(H) \subset \mathcal{H}$, generating the unitary one-parameter semigro …
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