Partially defined operator

In operator theory, a branch of mathematics, densely-defined or partially-defined operator is a linear operator defined on a dense set.

Let $X,Y$ be linear spaces. Let $A$ be a linear operator

$A: D(A) \subseteq X \to Y$

where $D(A)$ is domain of $A$ . Then, the operator $A$ is called densely-defined or partially-defined if $D(A)$ is dense in $X$ , in other words, if the closure of $D(A)$ coincides with $X$ .

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