Unbounded Normal Operators
The definition of normal operators naturally generalizes to some class of unbounded operators. Explicitly, a closed operator N is said to be normal if
Here, the existence of the adjoint implies that the domain of is dense, and the equality implies that the domain of equals that of, which is not necessarily the case in general.
The spectral theorem still holds for unbounded normal operators, but usually requires a different proof.
Read more about this topic: Normal Operator
Famous quotes containing the word normal:
“In order to move others deeply we must deliberately allow ourselves to be carried away beyond the bounds of our normal sensibility.”
—Joseph Conrad (18571924)