Could someone prove the following (if it is precisely correct):(adsbygoogle = window.adsbygoogle || []).push({});

Since Fock space is the closure of the finite linear span of finite excitations of the vacuum state $\Omega$, then the operator $\hat{O}$ is densely defined if and only if $\hat{O} \Omega$ has finite norm.

Or more generally, an operator is densely defined on a separable space if it is defined on a given single vector in that space.

thanks

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# Densely defined operators of Fock space

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