Positive element
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In functional analysis, a hermitian element A of a C*-algebra is a positive element if its spectrum consists of positive real numbers. Equivalently, A has a hermitian square root, that is an element B of the C*-algebra satisfying B*=B and B2=A.
If A is a bounded linear operator on a Hilbert space H, then this notion coincides with the condition that
- <math>\langle Ax,x\rangle<math>
be positive for every vector x in H.