Positive element

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In mathematics, especially functional analysis, a hermitian element A of a C*-algebra is a positive element if it is normal and 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

\langle Ax,x\rangle

be positive for every vector x in H.

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