A note on direct sums of quasinilpotent operators
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- by L. A. Fialkow PDF
- Proc. Amer. Math. Soc. 48 (1975), 125-131 Request permission
Abstract:
Let $\mathcal {Q}$ denote the set of all quasinilpotent operators on a fixed, separable Hilbert space $\mathcal {H}$. D. Herrero has found necessary conditions for an operator to belong to the norm closure of $\mathcal {Q}$ in $\mathcal {L}(\mathcal {H})$. We prove that each direct sum (or direct integral) of operators in ${\mathcal {Q}^ - }$ satisfies these conditions; two questions of D. Herrero are thereby related to one another. We also prove that the spectrum of a direct sum of nilpotent operators may be multiply connected.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 48 (1975), 125-131
- MSC: Primary 47A65
- DOI: https://doi.org/10.1090/S0002-9939-1975-0365201-5
- MathSciNet review: 0365201