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Julia operators and Halmos dilations

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arxiv 1803.09329 v1 pith:MCZA63BK submitted 2018-03-25 math.FA

P.L. Robinson This is my paper · ORCID
classification math.FA
keywords dilationshalmosjuliaunitarityassociatedcontractiondirectfollow
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abstract

We offer a simple direct proof of the unitarity of the Julia operator associated to a contraction $A$, from which follow the intertwining identity $(I - A A^*)^{1/2} A = A (I - A^* A)^{1/2}$ and the unitarity of Halmos dilations.

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  1. Gravitational redshift as a quantum channel: modeling the effects of gravitational redshift in quantum optics

    quant-ph 2026-08 conditional novelty 7.0 of 10

    Gravitational redshift cannot be represented by any finite set of smooth frequency modes, and the corrected finite-mode description is a Gaussian quantum channel built from a unitary dilation of the non-unitary compression.

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