On normal derivations
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- by Joel Anderson PDF
- Proc. Amer. Math. Soc. 38 (1973), 135-140 Request permission
Abstract:
Let ${\Delta _T}$ be the derivation on $\mathfrak {B}(\mathcal {H})$ defined by ${\Delta _T}(X) = TX - XT(T,X \in \mathfrak {B}(\mathcal {H}))$. We prove that if $T$ is an isometry or a normal operator, then the range of ${\Delta _T}$ is orthogonal to the null space of ${\Delta _T}$. Also, we prove that if $T$ is normal with an infinite number of points in its spectrum then the closed linear span of the range and the null space of ${\Delta _T}$ is not all of $\mathfrak {B}(\mathcal {H})$.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 135-140
- MSC: Primary 47B47; Secondary 47D99
- DOI: https://doi.org/10.1090/S0002-9939-1973-0312313-6
- MathSciNet review: 0312313