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.
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Famous quotes containing the word normal:
“A normal adolescent is so restless and twitchy and awkward that he can mange to injure his knee—not playing soccer, not playing football—but by falling off his chair in the middle of French class.”
—Judith Viorst (20th century)