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:
“Philosophically, incest asks a fundamental question of our shifting mores: not simply what is normal and what is deviant, but whether such a thing as deviance exists at all in human relationships if they seem satisfactory to those who share them.”
—Elizabeth Janeway (b. 1913)