Unitary polar factor of a finite compression
= Unitary polar factor of a finite compression
If $T_n=P_nAP_n^*$ is a square finite compression with <singular value decomposition> $T_n=V_n\Sigma_nW_n^*$, then $U_n=V_nW_n^*$ is a unitary extension of its polar factor. When $A$ is unitary and $P_n^*P_n\to I$ strongly, $|T_n|\to I$ strongly and hence $U_nP_n\to A$ strongly.