A note on the factorization of operator-valued functions

Nakazi, Takahiko

doi:10.1090/S0002-9939-1981-0601736-8

A note on the factorization of operator-valued functions
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by Takahiko Nakazi

Proc. Amer. Math. Soc. 81 (1981), 591-594

DOI: https://doi.org/10.1090/S0002-9939-1981-0601736-8

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Abstract:

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 ${\int _0^{2\pi } {\log || {T{{({e^{i\theta }})}^{ - 1}}} ||} ^{ - 1}}d\theta = - \infty$.

References

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Takahiko Nakazi, Extended weak-$^{\ast }$Dirichlet algebras, Pacific J. Math. 81 (1979), no. 2, 493–513. MR 547616