Functions of direct integrals of operators
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- by T. R. Chow and F. Gilfeather PDF
- Proc. Amer. Math. Soc. 29 (1971), 325-330 Request permission
Abstract:
This paper contains two results. The first one is that the unitary dilation of a direct integral of linear contraction operators is the direct integral of unitary dilations. For each linear contraction operator T on a Hilbert space, consider $f(T)$ as a bounded linear operator. The second result states that if $T = \smallint \oplus T(s)d\mu (s)$ is decomposable then so is $f(T)$ and $f(T) = \smallint \oplus f(T(s))d\mu (s)$.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 325-330
- MSC: Primary 47A60; Secondary 47B15
- DOI: https://doi.org/10.1090/S0002-9939-1971-0433239-1
- MathSciNet review: 0433239