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A simple proof of an extension of the Fuglede-Putnam theorem


Author: Wei Bang Gong
Journal: Proc. Amer. Math. Soc. 100 (1987), 599-600
MSC: Primary 47B20
DOI: https://doi.org/10.1090/S0002-9939-1987-0891172-7
MathSciNet review: 891172
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Abstract: A simple proof is given of the

Theorem. If $ A$ and $ {B^ * }$ are hyponormal, then $ {\left\Vert {AX - XB} \right\Vert _2} \geq {\left\Vert {{A^ * }X - X{B^ * }} \right\Vert _2}$ for every $ X$ in the Hilbert-Schmidt class.


References [Enhancements On Off] (What's this?)

  • [1] S. K. Berberian, Extensions of a theorem of Fuglede and Putnam, Proc. Amer. Math. Soc. 71 (1978), 113-114. MR 0487554 (58:7176)
  • [2] Takayuki Furuta, An extension of the Fuglede-Putnam theorem to subnormal operators using a Hilbert-Schmidt norm inequality, Proc. Amer. Math. Soc. 81 (1981), 240-242. MR 593465 (82e:47035)
  • [3] R. Schatten, Norm ideals of completely continuous operators, Springer-Verlag, Berlin, 1960. MR 0119112 (22:9878)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0891172-7
Keywords: Hyponormal operator, Hilbert-Schmidt class
Article copyright: © Copyright 1987 American Mathematical Society

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