Positive square root in a C-star algebra
= Positive square root in a C-star algebra
{title2=$a^{1/2}$}
Every <positive element of a C-star algebra> $a$ has a unique positive element $a^{1/2}$ satisfying $(a^{1/2})^2=a$. It is obtained by applying the continuous functional calculus to $t\mapsto\sqrt t$ on $\sigma(a)\subseteq[0,\infty)$.