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
Famous quotes containing the word positive:
“A positive learning climate in a school for young children is a composite of many things. It is an attitude that respects children. It is a place where children receive guidance and encouragement from the responsible adults around them. It is an environment where children can experiment and try out new ideas without fear of failure. It is an atmosphere that builds children’s self-confidence so they dare to take risks. It is an environment that nurtures a love of learning.”
—Carol B. Hillman (20th century)