Let us consider the commutative C*-algebra $C_0(\Omega)$. Let $\mu$ be a complex Radon measure on $\Omega$. By the Riesz representation theorem, $\mu$ may be considered as a bounded linear functional on $C_0(\Omega)$. The polar decomposition says that there is a partial isometry $u$ in the W*-algebra $C_0(\Omega)^{**}$ with $\mu=u|\mu|$.
Question: Is $|\mu|$ just the total variation of $\mu$?