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Proceedings of the American Mathematical Society

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



Functions of direct integrals of operators

Authors: T. R. Chow and F. Gilfeather
Journal: Proc. Amer. Math. Soc. 29 (1971), 325-330
MSC: Primary 47A60; Secondary 47B15
MathSciNet review: 0433239
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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)$.

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Keywords: Direct integrals, primary operators, dilations, strong operator measures and von Neumann algebras
Article copyright: © Copyright 1971 American Mathematical Society