Positive element of a C-star algebra
= Positive element of a C-star algebra
An element $a$ of a C-star algebra is positive when $a=b^*b$ for some $b$, equivalently when $a=a^*$ and $\sigma(a)\subseteq[0,\infty)$. Continuous functional calculus gives it a unique positive square root $a^{1/2}$.