Perturbations by nilpotent operators on Hilbert space
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- by Arlen Brown, Carl Pearcy and Norberto Salinas
- Proc. Amer. Math. Soc. 41 (1973), 530-534
- DOI: https://doi.org/10.1090/S0002-9939-1973-0374955-1
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Abstract:
If $T$ is any noncompact, bounded, linear operator on a separable Hilbert space $H$, then there exists a nilpotent (bounded, linear) operator $N$ on $H$ such that $N + T$ is invertible.References
- Arlen Brown and Carl Pearcy, Structure of commutators of operators, Ann. of Math. (2) 82 (1965), 112–127. MR 178354, DOI 10.2307/1970564
- John A. Dyer, Pasquale Porcelli, and Moshe Rosenfeld, Spectral characterization of two sided ideals in $B(H)$, Israel J. Math. 10 (1971), 26–31. MR 301524, DOI 10.1007/BF02771517
- Norberto Salinas, Operators with essentially disconnected spectrum, Acta Sci. Math. (Szeged) 33 (1972), 193–205. MR 350450
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 530-534
- MSC: Primary 47A55
- DOI: https://doi.org/10.1090/S0002-9939-1973-0374955-1
- MathSciNet review: 0374955