A bounded linear operator $A$ on a Hilbert space $H$ is called a positive operator if $\langle Ax, x\rangle \geq 0$ for all $x$ in $H$. It is known that, if $A$ is a positive operator on a Hilbert space $H$ over the complex field $\mathbb{C}$, then $A$ has unique positive square root.

My question is the following: Does a normal positive operator on an infinite dimensional Hilbert space over the real field $\mathbb{R}$ has a normal positive square root? If exist, is it unique?

A bounded linear operator $A$ on a Hilbert space $H$ is called a positive operator if $\langle Ax, x\rangle \geq 0$ for all $x$ in $H$. It is known that, if $A$ is a positive operator on a Hilbert space $H$ over the complex field $\mathbb{C}$, then $A$ has unique positive square root.

My question is the following: Does a normal positive operator on an infinite dimensional Hilbert space over the real field $\mathbb{R}$ have a normal positive square root? If it exists, is it unique?