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Positive matrix $ H\sp{1/2}$ and Hermitian matrix $ H\sp{1}$ functions are constant


Authors: H. Salehi and G. D. Taylor
Journal: Proc. Amer. Math. Soc. 26 (1970), 469-470
MSC: Primary 30.67
DOI: https://doi.org/10.1090/S0002-9939-1970-0267106-2
MathSciNet review: 0267106
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Abstract: It is known that if $ f \in {H^{1/2}}$ and $ f(z) \geqq 0$ a.e. for $ \vert z\vert = 1$ then $ f(z)$ is a constant. Also if $ f \in {H^1}$ and $ f(z)$ is real a.e. for $ \vert z\vert = 1$, then $ f$ is a constant. In this note we extend these two results to matrix-valued functions.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0267106-2
Keywords: Positive matrix functions, hermitian matrix functions, Hardy classes of functions
Article copyright: © Copyright 1970 American Mathematical Society

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