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:
“Everyone in the full enjoyment of all the blessings of his life, in his normal condition, feels some individual responsibility for the poverty of others. When the sympathies are not blunted by any false philosophy, one feels reproached by one’s own abundance.”
—Elizabeth Cady Stanton (1815–1902)