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A lifting theorem and analytic operator algebras


Author: Takahiko Nakazi
Journal: Proc. Amer. Math. Soc. 104 (1988), 1081-1085
MSC: Primary 47A20; Secondary 47D25
DOI: https://doi.org/10.1090/S0002-9939-1988-0969049-9
MathSciNet review: 969049
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Abstract: Let $ K$ be a complex Hilbert space and $ H$ a closed subspace. It is shown that if a $ 2 \times 2$ selfadjoint operator matrix $ T$ with positive diagonals on $ K \oplus K$ is positive on $ H \oplus {H^ \bot }$, then there exists a $ 2 \times 2$ operator matrix $ \tilde T$ with the same diagonals such that $ \tilde T$ is positive on $ K \oplus K$ and $ T$ is the restriction of $ \tilde T$ to $ H \oplus {H^ \bot }$. When $ T$ is in a von Neumann algebra, we consider the problems of finding $ T$ in the same algebra. This lifting theorem has applications to weighted norm inequalities for conjugation operators on analytic operator algebras.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0969049-9
Keywords: Commutant lifting, Arveson distance formula, factorization, Helson-Szegö theorem
Article copyright: © Copyright 1988 American Mathematical Society

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