A note on the factorization of operator-valued functions
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- by Takahiko Nakazi PDF
- Proc. Amer. Math. Soc. 81 (1981), 591-594 Request permission
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
- R. G. Douglas, On factoring positive operator functions, J. Math. Mech. 16 (1966), 119–126. MR 0209887, DOI 10.1512/iumj.1967.16.16007
- Allen Devinatz, The factorization of operator valued functions, Ann. of Math. (2) 73 (1961), 458–495. MR 126702, DOI 10.2307/1970313
- Henry Helson, Lectures on invariant subspaces, Academic Press, New York-London, 1964. MR 0171178
- Takahiko Nakazi, Extended weak-$^{\ast }$Dirichlet algebras, Pacific J. Math. 81 (1979), no. 2, 493–513. MR 547616
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 591-594
- MSC: Primary 47A68; Secondary 30H05, 46E40
- DOI: https://doi.org/10.1090/S0002-9939-1981-0601736-8
- MathSciNet review: 601736