An extension of the Fuglede-Putnam theorem to subnormal operators using a Hilbert-Schmidt norm inequality
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- by Takayuki Furuta PDF
- Proc. Amer. Math. Soc. 81 (1981), 240-242 Request permission
Abstract:
We prove that if $A$ and ${B^ * }$ are subnormal operators acting on a Hubert space, then for every bounded linear operator $X$, the Hilbert-Schmidt norm of $AX - XB$ is greater than or equal to the Hilbert-Schmidt norm of ${A^ * }X - X{B^ * }$. In particular, $AX = XB$ implies ${A^ * }X = X{B^ * }$. In addition, if we assume $X$ is a Hilbert-Schmidt operator, we can relax the subnormality conditions to hyponormality and still retain the inequality.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 240-242
- MSC: Primary 47B20; Secondary 47A05, 47B10
- DOI: https://doi.org/10.1090/S0002-9939-1981-0593465-4
- MathSciNet review: 593465