Positive Symmetric Operators
A symmetric operator A is called positive if <Ax, x> ≥ 0 for all x in Dom(A). It is known that for every such A, one has dim(K+) = dim(K-). Therefore every positive symmetric operator has self-adjoint extensions. The more interesting question in this direction is whether A has positive self-adjoint extensions.
For two positive operators A and B, we put A ≤ B if
in the sense of bounded operators.
Read more about this topic: Extensions Of Symmetric Operators
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