A note on the factorization of operator-valued functions

Devinatz showed the factorization of positive operator valued functions $T({e^{i\theta }})$ such that $\int _0^{2\pi } {\log } {|| {T{{({e^{i\theta }})}^{ - 1}}} ||^{ - 1}}d\theta > - \infty$. The purpose of this note is the factorization in case ${\int _0^{2\pi } {\log || {T{{({e^{i\theta }})}^{ - 1}}} ||} ^{ - 1}}d\theta = - \infty$.