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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on the factorization of operator-valued functions


Author: Takahiko Nakazi
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
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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 } {\vert\vert {T{{({e^{i\theta }})}^{ - 1}}} \vert\vert^{ - 1}}d\theta > - \infty $. The purpose of this note is the factorization in case $ {\int_0^{2\pi } {\log \vert\vert {T{{({e^{i\theta }})}^{ - 1}}} \vert\vert} ^{ - 1}}d\theta = - \infty $.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0601736-8
Keywords: Operator valued function, factorization, Hardy space, slice map, determinant
Article copyright: © Copyright 1981 American Mathematical Society