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A note on intertwining $ M$-hyponormal operators


Authors: R. L. Moore, D. D. Rogers and T. T. Trent
Journal: Proc. Amer. Math. Soc. 83 (1981), 514-516
MSC: Primary 47B20
MathSciNet review: 627681
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Abstract: If $ AX = X{B^ * }$ with $ A$ and $ B$ $ M$-hyponormal, then $ {A^ * }X = XB$. Furthermore, $ {({\text{ran}}\;X)^ - }$ reduces $ A$, ker $ X$ reduces $ B$, and $ A\vert{({\text{ran}}\;X)^ - }$ and $ {B^ * }\vert{\ker ^ \bot }X$ are unitarily equivalent normal operators. An asymptotic version is also proved.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0627681-X
Keywords: Normal operator, $ M$-hyponormal operator, intertwining
Article copyright: © Copyright 1981 American Mathematical Society