Partially-defined operator

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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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