Von Neumann's Formulas
Suppose A is symmetric; any symmetric extension of A is a restriction of A*; Indeed if B is symmetric
Theorem. Suppose A is a densely defined symmetric operator. Let
Then
and
where the decomposition is orthogonal relative to the graph inner product of dom(A*):
These are referred to as von Neumann's formulas in the Akhiezer and Glazman reference.
Read more about this topic: Self-adjoint Operator
Famous quotes containing the words von, neumann and/or formulas:
“You can put up with everything in this world except not with a long stretch of beautiful days.”
—Johann Wolfgang Von Goethe (1749–1832)
“It means there are times when a mere scientist has gone as far as he can. When he must pause and observe respectfully while something infinitely greater assumes control.”
—Kurt Neumann (1906–1958)
“That’s the great danger of sectarian opinions, they always accept the formulas of past events as useful for the measurement of future events and they never are, if you have high standards of accuracy.”
—John Dos Passos (1896–1970)