Krein's Theorem On Non-negative Self-adjoint Extensions
M. G. Krein has given an elegant characterization of all non-negative self-adjoint extensions of a non-negative symmetric operator T.
If T, S are non-negative self-adjoint operators, write
if, and only if,
Theorem. There are unique self-adjoint extensions Tmin and Tmax of any non-negative symmetric operator T such that
and every non-negative self-adjoint extension S of T is between Tmin and Tmax, i.e.
The Friedrichs extension of T is Tmax.
Read more about this topic: Friedrichs Extension
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