Diagonalizable normal operators
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- by J. P. Williams PDF
- Proc. Amer. Math. Soc. 54 (1976), 106-108 Request permission
Abstract:
If the image $\varphi (A)$ of a normal operator $A$ on a separable Hilbert space $\mathcal {K}$ is a diagonal operator for some nonzero representation $\varphi$ of $B(\mathcal {K})$ (that annihilates the compact operators), then $A$ must itself be a diagonal operator on $\mathcal {K}$ (with countable spectrum). This yields an โalgebraicโ characterization of the closure of the range of a derivation induced by a diagonal operator.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 106-108
- DOI: https://doi.org/10.1090/S0002-9939-1976-0397467-0
- MathSciNet review: 0397467