Positive operator

In mathematics, especially functional analysis, a self-adjoint (or Hermitian) element ${\displaystyle A}$ of a C*-algebra ${\displaystyle {\mathcal {A}}}$ is called positive if its spectrum ${\displaystyle \sigma (A)}$ consists of non-negative real numbers. Moreover, an element ${\displaystyle A}$ of a C*-algebra ${\displaystyle {\mathcal {A}}}$ is positive if and only if there is some ${\displaystyle B}$ in ${\displaystyle {\mathcal {A}}}$ such that ${\displaystyle A=B^{*}B}$. A positive element is self-adjoint and thus normal.

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