A lifting theorem and analytic operator algebras
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- by Takahiko Nakazi PDF
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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.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- 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