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On the class of norm limits of nilpotents


Author: Vasile Lauric
Journal: Proc. Amer. Math. Soc. 125 (1997), 3371-3379
MSC (1991): Primary 47A15, 47A65
DOI: https://doi.org/10.1090/S0002-9939-97-04012-4
MathSciNet review: 1415349
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Abstract: It is known that every operator on a Hilbert space $\mathcal {H}$ whose invariant subspace lattice is possibly $\{(0),\mathcal {H}\}$ is a norm-limit of a sequence of nilpotent operators. In this note we study properties of such approximating sequences.


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Additional Information

Vasile Lauric
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: lauric@math.tamu.edu

DOI: https://doi.org/10.1090/S0002-9939-97-04012-4
Keywords: Sequences of nilpotents, invariant subspaces
Received by editor(s): January 30, 1996
Received by editor(s) in revised form: June 26, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society